Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

This special issue of the Journal of Intelligent & Fuzzy Systems contains selected articles of fuzzy decision making and applications in knowledge management.

In this paper, we utilize induced Choquet ordered averaging operator to develop the induced hesitant interval-valued fuzzy choquet ordered averaging (IHIVFCOA) operator. Then, we have utilized this operator to develop the approach to solve the hesitant interval-valued fuzzy multiple attribute decision making problems. Finally, a practical example for evaluating the construction noise is given to verify the developed approach.

Einstein product is a t-norm and Einstein sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing triangular fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Einstein operations to develop some triangular fuzzy aggregation operators: triangular fuzzy Einstein weighted average (TFEWA) operator, triangular fuzzy Einstein ordered weighted average (TFEOWA) operator and triangular fuzzy Einstein hybrid average (TFEHA) operator. Then, we have utilized these operators to develop some approaches to solve the triangular fuzzy comprehensive evaluation problems. Finally, a practical example for evaluating the economic benefit evaluation of investment project of electric power enterprise is given to verify the developed approach.

 With respect to the decision making problems where the information of the attribute weights is incomplete under the intuitionistic fuzzy environment, a decision making method based on the improved VIKOR is developed. Firstly considering the advantage of the intuitionistic fuzzy set in expressing the decision makers’ preference information, the intuitionistic fuzzy evaluation matrices are established. In order to derive the attribute weights from the incomplete attribute information of weights, a linear programming model is proposed. Then the traditional VIKOR method is improved by replacing the distance measure with projection model. Finally an illustrative example is given to prove the practicality and effectiveness of the method proposed.

Based on the concept of environmental carrying capacity and airport capacity, in this paper we propose the concept of airport environment capacity (AEC). We calculated the maximum pollutant concentration in an airport by constructing a pollutant evaluation model, established the relationship between the pollutant concentration and the sorties of aircraft taking off and landing, and provided a method of determining the AEC. Using Shanghai Pudong International Airport as an example, we evaluated AEC according to the proposed evaluation method and process. The result showed that the evaluation method was correct and effective.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The interval-valued intuitionistic fuzzy sets (IVIFSs) are useful tools to depict uncertainty of the MADM. In this paper, we will extend TODIM method to the MADM with the interval-valued intuitionistic fuzzy numbers (IVIFNs). Firstly, the definition, comparison and distance of IVIFNs are introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, the extended classical TODIM method is proposed to deal with MADM problems with the IVIFNs, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Finally, a numerical example for performance appraisal on social-integration-based rural reconstruction is proposed and a comparative analysis is also given.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

In recent years, construction of urban space in China likes a ranging fire, which effectively improves urban habitats. However, serious problems appear incessantly among decisions, layout, designs, development and management of public space in China. In terms of urban common space in individual city, it exits quality decline, structure illegibility and regression of functions and artistic appearances, which are what we need to keep away and improve on. In this paper, we study the problem of multiple attribute decision making for evaluating the impact of mobile phone information technology on the urban public space development under the internet background in which the decision making information values are interval number, a new decision making method is proposed. Then, according to the concept of the cross entropy, the relative closeness degree is defined to determine the ranking order of all alternatives by calculating the cross entropy to both the interval positive-ideal solution (IPIS) and interval negative-ideal solution (INIS) simultaneously. At last, a numerical example for evaluating the impact of mobile phone information technology on the urban public space development under the internet background is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

We study on the multiple attribute decision making problems using the hesitant triangular fuzzy information. Afterwards, we have designed the hesitant triangular fuzzy generalized Bonferroni Mean (HTFGBM) operator and hesitant triangular fuzzy generalized weighted Bonferroni Mean (HTFGWBM) operator. We have utilized the HTFGBM and HTFGWBM operators to multiple attribute decision making for evaluating the finance achievements of the transnational corporation with hesitant triangular fuzzy information. In the end, an illustrative example for evaluating the finance achievements of the transnational corporation is proposed to demonstrate the effectiveness of our proposed method.

In this paper, we shall present some novel Dice similarity measures of 2-tuple linguistic variables and the generalized Dice similarity measures of 2-tuple linguistic variables and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with 2-tuple linguistic variables. Then, we apply the generalized Dice similarity measures between 2-tuple linguistic variables for evaluating the development level of the mass sports culture organization. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for evaluating the development level of the mass sports culture organization.

 In this paper, we investigate the multiple attribute decision making problems for evaluating the management performance for the transnational corporation with 2-tuple linguistic information. Motivated by the ideal of generalized weighted Bonferroni mean and dual generalized weighted Bonferroni mean, we develop the 2-tuple linguistic generalized Bonferroni mean (2TLGBM) operator and the 2-tuple linguistic dual generalized Bonferroni mean (2TLDGBM) operator for aggregating the 2-tuple linguistic information. For the situations where the input arguments have different importance, we then define the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator and the 2-tuple linguistic dual generalized weighted Bonferroni mean (2TLDGWBM), based on which we develop the procedure for multiple attribute decision making under the 2-tuple linguistic environments. At last, a numerical example for evaluating the management performance for the transnational corporation is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

 A new category of similarity measures is investigated in this work, we first introduce the concept of effect matrix T ∧ ( R 1 × R 2 , p n , q m ) of type 2-tuple and study some of their properties. Moreover, from the soft set we find the pictures of type regular and irregular using effect matrix T ∧ ( R 1 × R 2 , p n , q m ) of type 2-tuple. An effect matrix T ∧ ( R 1 × R 2 , p n , q m ) of type 2-tuple is better than effect matrix E ∧ ( R , p n , q m ) of type 1-tuple, because we can deal with two different sets R 1 (a family of objectives) and R 2 (a family of parameters) in the same problem. This burden can be alleviated by application of type 2-tuple. Some applications of soft effect matrix of type 2-tuple T ∧ ( R 1 × R 2 , p n , q m ) in decision making problems are studied and explained. In this work we deal with pictures. Moreover, the similarity measure between two different soft sets under the same universal soft set ( R 1 × R 2 ) can be studied and explained its applications in medical diagnosis problems.

 Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with vagueness and uncertainties. It is worth noting that the decision making theory has been proven a more effective tool in the real-world problems under imprecise environments. In this paper, we introduce a new fuzzy soft model, called the multi-fuzzy bipolar soft set model. Some operations of this notion are first investigated and some of the related properties are studied. Finally, an algorithm based on multi-fuzzy bipolar soft set is presented and an illustrative example is given to analyze the application of the proposed algorithm.

It is widely acknowledged that a corporate’s profitability that decreases dramatically not only threatens both potential and current investors, but also can freeze stock market transactions as well as deteriorate the flow of economic resources. However, far too little attention has been paid to this issue, which also has been deemed as a main trigger for a financial crisis. To confront this problem, a decision support system can be built up to evaluate a corporate’s operating performance. Thus, this study introduces a novel architecture for forecasting the online operating performance of a firm when entering data at different time intervals. The introduced architecture is grounded on multiple data envelopment analysis specifications, dynamic fuzzy c-means (DFCM), and extreme support vector machine (ESVM). Because obtaining a comprehensible architecture is essential for achieving high accuracy in today’s knowledge-based economy, this study advances the opaque nature of the introduced architecture and extracts the inherent knowledge to represent it in a transparent, human-readable format. The decision logics can be judged or examined by users, which will increase the acceptance rate of the architecture as well as enhance its practical application. Our built-up architecture, tested by real cases, is a promising alternative for financial performance forecasting.

Fuzzy cognitive maps (FCM) and Bayesian belief networks (BBN) are two of the most frequently used causal knowledge frameworks for modelling, representing and reasoning about causal knowledge. In this paper, an evaluation of their different roles in the engineering process of developing causal knowledge systems is conducted, based on their inherent features. The evaluation criteria adopted in this research are understandability, usability, modularity, scalability, expressiveness, inferential capability, rigour, formality and preciseness. All of these are commonly used to evaluate the strengths and weaknesses of traditional knowledge representation frameworks. These criteria are used to reveal the fundamental characteristics of FCM and BBN. The findings of this study show that FCM is more appropriate for use in modelling causal knowledge, whereas BBN is more superior in model representation and inference. This study deepens the understanding of the role of FCM and BBN in the development of causal knowledge systems.

In this paper, we investigate the MSM operator and extend the MSM operator to interval-valued intuitionistic fuzzy environment and develop the interval-valued intuitionistic fuzzy Maclaurin symmetric mean (IVIFMSM) operator. Using IVIFMSM operator, a novel algorithm to MADM problems by utilizing interval-valued intuitionistic fuzzy information is developed. In the end, we provide an example for evaluating the foreign trade sustainable development is given.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

In this paper, we proposed the 2-tuple linguistic VIKOR method based on the fundamental theories of 2-tuple linguistic information and origin VIKOR model. Firstly, we introduce the concepts, operation formulas and the distance calculating method of 2-tuple linguistic information. Then we review some aggregation operator of 2-tuple linguistic number, thereafter, the calculating steps of the VIKOR model for 2-tuple linguistic MCGDM problems are simply presented, in our proposed method; it’s more scientific and reasonable for considering the conflicting attributes. Moreover, a numerical example for effect evaluation of ancient village landscape planning based on the heritage historical context has been proposed to illustrate the new method and some comparisons are also conducted to further illustrate advantages of the new method.

In this paper, we investigate the multiple attribute decision making (MADM) problems with triangular fuzzy information. Motivated by the ideal of dual generalized Bonferroni mean and dual generalized geometric Bonferroni mean, we develop two aggregation techniques called the dual generalized triangular fuzzy Bonferroni mean (DGTFBM) operator and the dual generalized triangular fuzzy geometric Bonferroni mean (DGTFGBM) operator for aggregating the triangular fuzzy information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the dual generalized triangular fuzzy weighted Bonferroni mean (DGTFWBM) operator and the dual generalized triangular fuzzy weighted geometric Bonferroni mean (DGTFWGBM) operator, based on which we develop two procedure for multiple attribute decision making under the triangular fuzzy environments. Finally, a practical example for hotel supply chain risk assessment is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we study the problem of multiple attribute decision making for evaluating the art education teaching quality in which the decision making information values are interval number, a new decision making method is proposed. Then, according to the concept of the cross entropy, the relative closeness degree is defined to determine the ranking order of all alternatives by calculating the cross entropy to both the interval positive-ideal solution (IPIS) and interval negative-ideal solution (INIS) simultaneously. At last, a numerical example for evaluating the art education teaching quality is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

In this paper, we investigate the picture fuzzy multiple attribute decision making problems where the information about attribute weights is partly known or completely unknown. We introduce some notions, such as picture fuzzy ideal point, the normalized Hamming distance of picture fuzzy numbers. We also introduce the grey relational coefficient between the attribute value vectors of each alternative and the picture fuzzy ideal point. Then we establish the grey relational analysis models to measure the grey relational degree between each alternative and the picture fuzzy ideal point. Based on the grey relational analysis models, we can rank the given alternatives and then select the most desirable one. Finally, we illustrate the developed grey relational analysis models with a numerical example for potential evaluation of emerging technology commercialization.

In this paper, we study on the multiple attribute decision making problems for evaluating the competitiveness of high technological parks with triangular fuzzy information. Inspired by the idea of Bonferroni mean (BM) and geometric Bonferroni mean (GBM), we develop the triangular fuzzy power Bonferroni mean (TFPBM) operator, triangular fuzzy weighted power Bonferroni mean (TFWPBM) operator, the triangular fuzzy power geometric Bonferroni mean (TFPGBM) operator, triangular fuzzy weighted power geometric Bonferroni mean (TFWPGBM) operator. Using the proposed operator, we propose the program for multiple attribute decision making with the triangular fuzzy environments. In the end, a practical example for evaluating the competitiveness of high technological parks with triangular fuzzy information is given to testify the performance of the given approach.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434.

This article has been retracted, and the online PDF has been watermarked “RETRACTED”. A retraction notice is available at https://doi.org/10.3233/IFS-219217.

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviors under risk, has been introduced to handle multiple attribute decision making (MADM) problems. Moreover, 2-tuple linguistic term set is an effective tool for depicting uncertainty of the MADM problems. In this paper, we will extend the TODIM method to the MADM with the 2-tuple linguistic information. Firstly, the definition and distance of 2-tuple linguistic information are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the 2-tuple linguistic information, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Finally, a numerical example for evaluating the service quality of boutique tourist scenic spot is proposed to verify the developed approach and its practicality and effectiveness.

The probabilistic fuzzy set (PFS) is designed for handling uncertainties with both fuzzy and stochastic nature, so the probabilistic fuzzy logic system (PFLS) has the ability to handle more complex uncertainties in process. In this paper, the general probabilistic fuzzy set is proposed, and the convergence analyses of its secondary probability density function (PDF) are conducted. It discloses the distribution regularity of membership degree in general PFS, which improves the information and interpretability of PFS. Then, according to convergence, a new method to tuning parameters for PFLS is proposed. This method avoids the parameters into local inefficiency, and also reduces the number of learning parameters in PFLS. Last, the new tuning method is applied to the electromyography (EMG) robots modeling problem. The comparison shows that the probabilistic fuzzy logic system based on general PFS (GPFLS) can achieve a simple modeling process, and also, it improves the learning speed compared to PFLS. The work presented will improve the potential application of probabilistic fuzzy logic system.

The risk assessment of roof water inrush is of great significance for sustainable development of mine and ecological environment. Taking the Jurassic coalfield in northwest China as an engineering background, we firstly selected nine indexes influencing roof water inrush based on three essential conditions with the water source, the water inrush channel and the mining space, i.e., unit water inflow, flushing fluid consumption, aquifer thickness, effective aquiclude thickness, lithological association of the effective aquiclude, inclined length of coalface, buried depth of coal seam, mining thickness and advancing speed of coal mining, and then established the hierarchy structure model for mutation evaluation of roof water inrush. Secondly, the expert scoring method and trapezoidal fuzzy distribution were chosen to construct the initial fuzzy membership function based on the characteristics with fuzziness and mutability of roof water inrush. Thirdly, based on quantized recursion operation with the normalization formula and the (non) complementarity principle, total mutation membership function value was calculated, and the water inrush risk grade was determined. Eventually, the proposed method has successfully predicted the water inrush risk in the first mining face of Jinjitan coal mine. The research achievements provide an important reference for the sustainable development of the Jurassic coalfield.

In this paper, we introduce the co-annihilator ^⊥A of a set A and the co-annihilator of (F : a) of a relative to a prefilter (filter) F in an EQ-algebra ɛ. We investigate related properties of them, and obtain that the lattice of all prefilters PF ( ɛ ) forms a pseudo-complemented lattice and the collection of all co-annihilators COA ( ɛ ) forms a Boolean algebra in a separated EQ-algebra ɛ. Moreover, we introduce the notion of Δ-co-annihilators in an EQ_Δ-algebra ɛ_Δ and conclude that the collection of all Δ-prefilters PF Δ ( ɛ Δ ) in an ℓEQ_Δ-algebra ɛ_Δ constitutes a relative pseudo-complemented lattice. Finally, we introduce and investigate two types of fuzzy co-annihilators Ann _R  (μ) and Ann (μ, ν) in ɛ. We come to a conclusion that the set of all fuzzy filters FF ( ɛ ) in a residuated ℓEQ-algebra ɛ forms a relative pseudo-complemented lattice whence → is the Gödel residuated implication in St ^r  (μ, ν).

Video retrieval technology has drawn considerable attention over the years. Compared with the underlying information such as color, edge, etc., the text in the video contains rich semantic information and can well summarize the video information. Many scholars have proposed methods based on SVM to detect video text. For most of these methods, feature dimension is too large, and the time complexity and detection effect remain to be improved. In this paper, a new method of SVM video text detection based on color, edge and HOG features is proposed. And for the problem of single frame detection, the detection effect is improved based on the detection of three adjacent frames. In this paper, video text detection is implemented through steps such as sample selection, feature extraction, model training, and text detection. Finally, many experiments are performed to compare the proposed method with other literatures. The results show that the proposed single-frame and three-frame detection algorithm has a high recall rate and accuracy, which reduces the false detection rate and improves the effectiveness of video text detection.

Prediction of links/ connections in social networks is useful for increasing business in the area of telecom and social media. All types of social networking organization are trying to increase their nodes, i.e. the number of members. So the calculation of link prediction is the most important task because this calculation will help how to increase the number of user on a social network. A new technique of link prediction, namely RSM index, is introduced in this paper. Few essential properties have been established. Also, a comparative study with the existing methods is depicted with suitable tables and graphs.

Different aspects of social networks have increasingly been under investigation from last decade. The social network studies range in various viewpoints from the structural and node measures to the information diffusion processes. Key node identification has been one of the limelight topics of social network analysis (SNA) specifically in a discipline like politics, criminology, marketing etc. This research uses multiple networks constructed from the different social site and real-life relationships to cover the multi-dimensional aspects of human relations. In the multi-relationship system, the different dimensions may differ in terms of relevance and weight. One of the most intriguing aspects of key node identification in the multi-dimensional system can be the consideration of dimension relevance. This research covers the methodology to optimize the weights of dimensions using a number of centrality measures from each network layer covering multiple different objectives of interest. The study formulates the novel weighted feature set pertaining to layer relevance calculated based on layers relative importance through particle swarm optimization technique. The framework applies ensemble-based approach on the weighted feature set along with node characteristics to predict key nodes in a network. The results are validated against ground truth data and accuracy achieved is promising.

 Accurate and fast islanding detection of distributed generation is extremely important for its effective operation in distribution systems. For this purpose, several islanding detection methods have been suggested. Among them, hybrid islanding detection techniques are preferred due to their minimum effects on the power system. However, hybrid islanding detection techniques also suffer from two main limitations. They still degrade the power quality and also take comparatively large time to detect the islanding phenomenon. Thus, fast detection and power quality degradation issues are still not solved by hybrid islanding detection techniques. To address this issue, this paper suggests a new islanding detection technique based on rate of change of reactive power (ROCORP) and radial basis function neural network (RBFNN). The proposed technique uses ROCORP as the RBFNN input. The appropriate database of several islanding and non-islanding events is generated by performing the offline simulations on 26 Bus Malaysian distribution system for training the RBFNN. The simulation results shows that it can detects islanding and non-islanding events very fast without degrading the power quality of the system and is independent of threshold limitations.

In recent years, multiple robots have been successfully applied in various fields, including the handling of logistics factories, agriculture, and disaster relief. This study proposes a novel method for multi-robot deployment and navigation in dynamic environments. To address the problem of location deployment, a grid-based method was used to simplify environmental input information, and a self-clustering method was used to adjust location deployment. To address the problem of navigation, a behavior manager was used as a navigation strategy to control the towards-goal behavior and wall-following behavior (WFB) of mobile robots. An interval type-2 fuzzy controller based on improved particle swarm optimization (IPSO) was proposed to implement the WFB control. The proposed IPSO improved the search ability and enhanced the convergence speed of traditional PSO. Additionally, an escape mechanism was proposed to avoid a dead cycle. Experimental results show that the proposed IPSO is superior to other methods used for WFB and navigation control.

The goal of this paper is to introduce the concept of λ-statistical convergence of weight g of fuzzy numbers by using ideal. In addition to this concept, some inclusion theorems are also presented.

In this paper, a general type-2 fuzzy logic controller (GT2FLC), which is optimized by the particle swarm optimization (PSO) algorithm, is applied to a power-line inspection (PLI) robot. The information fusion is used to design the GT2FLC to avoid the rule explosion. The proposed controller has the ability to deal with uncertainties when the PLI robot works on the insulated access cable. In order to compare the performance of the proposed controller with that of other controllers, the type-1 fuzzy logic controller (T1FLC) and the interval type-2 fuzzy logic controller (IT2FLC) are both optimized by the PSO to adjust the PLI robot. To show the ability of different controllers to deal with uncertainties, external disturbances and parameter perturbations are added to the PLI robot. According to simulations, the performance of the proposed controller is better than that of other controllers, and the proposed controller has better ability to deal with uncertainties.

The route length is taken by the operator is deemed to be an effective parameter in minimization of response time’s orders in a typical warehouses with a manual picking system, in which the picker collects goods through depot. Therefore, reduction of the route length has been increasingly received considerable attention from the scholars in this area. The response time and system’s costs are regarded as the most essential components necessitating the utilization of order batching process for rival companies, particularly when there is no information about time and amount of inbound orders, and even when there is substantial amounts of orders in large warehouses working with an online order entry system. This process has a profound impact on reducing the route length and thus decreasing the organization costs. Present study takes aim at investigation of order classification in the first time in the picker-to-part system as a manual picking system and an online order batching system, with the intent of minimizing the turnover time and idle time. Besides, an order batching model in a blocked warehouse using a zoning system is proposed which is called Online Order Batching in Blocked Warehouse with One Picker for each Block (OOBBWOPB). This is investigated by online order entry system using a nonlinear programming model based on meta-heuristic method of Teaching Learning Based Optimization (TLBO) algorithm. The average turnover time of the customer’s orders is witnessed insignificant reduction using the proposed model, which lead to greatly enhance the total efficiency of warehouse system.

Dempster-Shafer theory (DST) of evidence has wide application prospect in the fields of information aggregation and decision analysis. To solve the issues of interval evidence combination and normalization, we have reinvestigated the methods provided for interval evidence combination within the frameworks of DST and evidential reasoning (ER) approach, respectively, and pointed out the shortcomings of existing methods. A more general interval evidence combination approach based on the ER rule is constructed. Numerical examples are provided to indicate that the proposed method not only suitable to the conflict-free interval evidence combination, but also to the conflicting interval evidence combination, and interval evidence specificity can be kept intact in the interval evidence combination process. Moreover, the interval evidence combination methods based on DST or ER are special cases of the proposed method in some cases.

In this paper we present a new algorithm called Neural Network Pruning Based on Input Importance (NNPII) that prunes the neural network based on the input importance. The algorithm depends on the frequency of using a certain value of an attribute in all the given instances in the dataset. Pruning will include only links between input layer and hidden layer. The algorithm has three phases, the first phase is the preprocessing phase, where the data inputs are replaced with their importance. The second phase is a forward pass, which is similar to forward pass in the backpropgation algorithm, but instead of using the real inputs as inputs, we use the input importance obtained in the preprocessing stage. The third pass is the backward phase which is again as backpropgation algorithm, but in this stage we use the input importance instead of real inputs, and β factor that measures the value changing for every input attribute, β will be incorporated in the formula in updating the weights between the input layer and the hidden layer. The elimination process is performed based on criterion that depends on Ω factor that represents a threshold value for a certain input attribute for all instances. It is worth mentioning that the pruning is performed within the usual training phases. The proposed algorithm has been tested through three types of experiments, a comparison between backpropgation and NNPII, Applying NNPII with various parameter values and finally comparing NNPII with other various pruning algorithms. Results show that NNPII performs well and compete with other pruning algorithms. NNPII outperforms all other algorithms when the classes are fairly distributed in the datasets.

In this paper, the notions of L-fuzzy convex subgroup and L-fuzzy convex subgroup degree are introduced and their characterizations are given. A new method for describing L-fuzzy convexity is obtained. Also, L-fuzzy convexity preserving mappings and L-fuzzy convex-to-convex mappings are analyzed. Besides, we provide a counter example to illustrate one of the conclusions.

By using the residual implication on a frame L, a degree approach to special mappings in L-convex spaces and L-interval spaces is introduced. In the framework of L-convex spaces, degrees of L-CP mappings and L-CC mappings between L-convex spaces are defined. Also, in the situation of L-interval spaces, degrees of L-IP mappings and L-AIP mappings are proposed. Moreover, many conclusions with respect to theses mappings are discussed in a degree sense.

 A method for image edge detection is proposed, which employs interval-valued fuzzy (IVF) sets such that each pixel has an interval membership constructed from its original and neighboring intensities. This method relies on triangular norms and co-norms to develop operators generating lower (LIB) and upper (UIB) interval bounds, which are employed in a novel membership function. This membership function is then applied to the image represented as fuzzy singletons to generate an image containing the edges associated with the original image. The proposed method is applied to medical images for edge detection and the results are compared with those obtained based on application of other fuzzy methods as well as a classical method for implementation of edge detectors. The quantitative comparison of the edge binary images determined by each method is performed by employing a metric based on the Hausdorf distance as well as a metric based on the local refinement error known as global consistency error (GCE). The proposed method consistently produced lower values of Baddeley’s Delta metric as well as lower values of GCE. The proposed method was also characterized by values of Pratt’s figure of merit closer to unity as compared with the other methods. Furthermore, the proposed method outperforms a number of commonly employed edge detectors in terms of the processing time required for edge detection.

 Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated.

Substantial improvements are being every day made in decisions quality by introducing new Multi Criteria Decision Making (MCDM) methods. Due to the ambiguity in decision data, obtaining the real value of the criteria for modeling multi criteria decision making problems is very important. On the other hand, the challenges associated with the selection of sustainable suppliers will make managers and experts to develop and improve new decision-making methods to solve these challenges. Therefore, fuzzy best-worst method (FBWM) is used to weigh supplier selection criteria and then piecewise linear values function is used to rank suppliers in this paper. The proposed method addressed the problem of sustainable supplier selection in the oilseed industry as a case study in food supply chain. The findings of the suggested methodology showed that although the results of applying exponential and piecewise linear value function are somehow close to each other, compared with simple integrated functions using appropriate value functions can produce more reliable results and have a great impact on the performance of MCDM problems.

This paper describes a method to extract the cardiac vessels in coronary angiography images. The cardiac vessel extraction technique is a significant process in clinical scenario for cardiac image analysis of Coronary Computed Tomography Angiography (CCTA) datasets. CCTA is a speedy growing non-invasive cardiac imaging modality that provides vital diagnostic information for the cardiac disease diagnosis. Since cardiac vessel extraction for CTA images is a prime issue in computer-aided medical diagnosis, algorithms or systems for vessel detection are always demanded. In order to support computer-aided diagnosis, a modified Frangi’s vesselness measure based on gradient and grayscale measure of the cardiac images is proposed in this work. The experimental result shows that the proposed method can effectively enhance vascular structures and suppress the pseudo vascular structures. It eliminates the background noise and helps in separation of neighboring vessels. The proposed vesselness measure were statistically analyzed by analysis of variance (i.e) one-way ANOVA. The statistical analysis also proves that the proposed vesselness measure based on gradient and grayness values extracts the vessel segments more effectively from the background. Hence the method detects the cardiac vessels more effectively by incorporating the fact that the gradient and grayscale values are comparatively different inside and outside the cardiac vessels. The proposed method has been evaluated on 3D CCTA images and the results are promising.

Environmental governance cost prediction is an essential process in environmental protection. However, the existing environmental governance cost prediction methods are facing two challenges: First, the principal components of environmental indicator information must be accurately extracted without considering the independence of environmental indicators. Second, the higher interpretability and the lower complexity must be taken into account with the desired accuracy for improving the cost prediction of environmental governance. Therefore, the fuzzy rule based system (FRBS) and feature extraction are introduced to propose a new environmental governance cost prediction method, named FRBS-FE, in which the feature extraction is used to extract the principal components of environmental indicator information firstly, and then all these principal components are applied to generate a FRBS-FE for better environmental governance cost prediction. A case study involving 29 provinces of China is carried out to demonstrate the effectiveness of the FRBS-FE. The results showed that the FRBS-FE not only can accurately predict different kinds of environmental governance costs, but also have superior performance in comparison with previous cost prediction methods.

Denoising of medical image modalities is one among the foremost basic issues in medical image process. Medical modalities such as ultrasound images suffer from multiplicative speckle noise. This noise consequently reduces the contrast of ultrasound images and adversely affects the other medical image processing tasks such as medical image registration, image super-resolution, and image segmentation. Therefore, one of the important objectives of any denoising algorithm is to attenuate the speckle noise effectively and also preserve the significant medical details in the denoised image. The main focus of this paper is the reduction of speckle noise for ultrasound images using various similarity measures in non-local framework. Through exhaustive experiments conducted on real ultrasound images, B-mode and simulated synthetic images demonstrate that, the Square chord and Chi-square distance-based similarity measures are the most effective similarity measure used in non-local framework for denoising of ultrasound images.

The grey wolf optimizer (GWO) algorithm is a recently proposed optimization technique based on the social leadership and hunting behavior of grey wolves in nature. Due to its small number of control parameters, ease of implementation and high level of exploration and exploitation, the GWO has attracted the interest of researchers from different fields. However, the GWO has problems with its position-updated equation, which is good for exploitation but not conducive to exploration because it can prematurely convergence to local optima. To overcome this drawback, a chaotic dynamic weight grey wolf optimizer (CDGWO) is proposed. In the CDGWO algorithm, a new position-updated equation is presented by applying a chaotic map and dynamic weight to guide the search process for potential candidate solutions. In addition, a nonlinear control parameter strategy is designed to balance the exploration and exploitation and accelerate the convergence speed of the GWO algorithm. The search accuracy and performance of the modified position-updated equation and the nonlinear control parameter strategy are verified using 19 well-known classical benchmark functions. The experimental results show that, for almost all benchmark functions, the CDGWO algorithm gives competitive results in terms of convergence, solution quality and local optimal avoidance compared with other nature-inspired optimizations and GWO variants.

Horizontal cooperation in logistics refers to several logistics service providers cooperating to accomplish common goals, which usually involves a collaborative vehicle routing problem. In this paper, we present a new collaborative vehicle routing problem with rough location (CVRPRL), which considers both the security of sharing detailed customer information and the configuration of shared resource. We utilize the rough location of the customer to replace the detailed customer location and introduce the concept of collaborative logistics sharing degree in the CVRPRL model. Subsequently, the cost allocation mechanism is designed based on an extended Shapley value, which allocates fixed costs and risks in different ways. Further, an extended ant colony optimization (EACO) algorithm is proposed to solve the CVRPRL. The EACO algorithm combines both large neighborhood search and local search strategies. Finally, we perform a series of simulation experiments to verify the effectiveness of EACO compared with other meta-heuristic algorithms.

In this paper we propose a new approach to the fuzzification of lattices, which is defined from the view of algebraic structure. It is also called an M-hazy lattice. Some properties of M-hazy semilattices and M-hazy lattices are discussed. Besides, we also discuss its relations with M-fuzzifying interval spaces and M-fuzzifying convex spaces.

 Apart from other labeling signed product and total signed product labeling already have been applied on different kind of graphs. Signed product cordial labeling for the graph G = (V, E), where each vertex is labelled by 1 or -1 and edge label is induced by multiplication of two of it end vertices with the following restriction that the absolute difference between total number of vertices labelled by 1 and -1 is at most 1, similarly for the edges also. Total signed product cordial labeling follows property that absolute difference between total number of vertices and edges labelled by -1 and total number of vertices and edges labelled by 1 is at most 1. In this paper, we have considered Cartesian product between two balanced bipartite graphs and apply above labeling on it. We have designed some suitable algorithms which will driven by any kind of computer programming language. Illustration with example and complexity of the algorithms are analysed successfully.

With the enhancement of the global environmental awareness, green supplier selection is playing an increasingly important role in the development of enterprises. Green supplier evaluation criteria include quantitative and qualitative criteria. Due to the complexity and ambiguity of actual decision making problems, and the subjectivity of decision makers (DMs), it is difficult to describe qualitative criteria with precise data. In this paper, Pythagorean fuzzy numbers (PFNs) are used to describe the qualitative criteria, then a data envelopment analysis (DEA) model with undesirable outputs under Pythagorean fuzzy environment is developed. Finally, a numerical example ahout green supplier selection is provided to demonstrate the usefulness of the proposed method.

The well-known Fuzzy C-Means (FCM) algorithm and its modified clustering derivatives have been widely applied in various fields. However, previous studies have focused on the yield of correctly clustered data, and few have addressed the alignment of extracted influential areas of clusters to natural cluster structure. Various clustering algorithms present diverse characteristics in cluster structure detection due to the different clustering principles involved. For example, Mahalanobis distance-based FCM algorithms effectively detect the influential direction of each cluster, while kernel-based FCM algorithms provide an interface for adjusting the influential range. Combining the advantages of these previous algorithms, the Adaptive Kernel Fuzzy C-Means (AKFCM) algorithm based on cluster structure is proposed in this paper. The AKFCM algorithm can effectively detect the influential direction and adjust the influential range of each cluster with adaptive kernelization. By applying the previous and AKFCM algorithms to both synthetic and real-world datasets, the proposed algorithm is proven to achieve better performance not only in clustering accuracy but also in the extraction of reasonable influential areas. The proposed algorithm could be helpful for clustering datasets composed of clusters with different directions and ranges in structure.

A huge range of human decisions is involved bipolar subjective thoughts. For illustration, effects and side effects are two different aspects of decision analysis. The equilibrium and mutual coexistence of these two aspects are treated as a key for balanced social environment. A verity of bipolar fuzzy decision making with different technique is available for bipolar fuzzy characterizations of the universe of options that depend on a limited number of grades. So, the concept of simple bipolar fuzzy set is insufficient to provide the information about the occurrence of ranking with accuracy because information is limited. In this regard, we use cubic bipolar fuzzy sets (CBFSs) as the generalization of bipolar fuzzy sets. In human decisions, the second important part is ranking of alternatives obtained after evaluation. The motivation behind this research is to develop an appropriate aggregation method which is simple reliable and efficient enough to handle cubic bipolar fuzzy data. We propose aggregation operators, including, cubic bipolar fuzzy weighted averaging operator, cubic bipolar fuzzy ordered weighted averaging operator and cubic bipolar fuzzy hybrid weighted averaging operator for P -order and R -order. We demonstrate simplicity and efficiency of proposed aggregation operators and algorithm by discussing multi-attribute group decision making (MAGDM) problem under cubic bipolar fuzzy information. We also discuss the comparison analysis of the proposed method of aggregation.

 In this paper, we consider a type of fuzzy harmonic oscillator described by a differential equation of the form x″ + a²x = 0 with initial conditions given by fuzzy numbers. Here, we assume that x″ (t) and a²x (t) are linearly correlated fuzzy numbers for t ∈ ℝ and a ∈ ℝ , a ≠ 0 . In general, this assumption is necessary for the equality x″ + a²x = 0 to make sense. Using this interactive relation, we obtain a solution for this problem using a fuzzy Laplace transform method.

Deep convolutional neural networks (CNNs) have shown outstanding performance in salient object detection. However, there exist two conundrums under-explored. 1) High-level features are beneficial to locate salient objects while low-level features contain fine-grained details. How to combine these two types of features to promote accuracy is the first conundrum. 2) Previous CNN-based methods adopt a convolutional layer after extracting features to infer saliency maps. While encountering images that are different greatly from training dataset, adopting a convolutional layer as a classifier is not robust enough to detect all salient objects. In addition, limited receptive field and lack of spatial correlation will cause salient objects to be incomplete while blurring their boundaries. In this paper, a Lateral Hierarchically Refining Network (LHRNet) is put forward for accurate salient object detection. Firstly, LHRNet efficiently integrates multi-level features, which simultaneously incorporates coarse semantics and fine details. Then a coarse saliency prediction is made from low-resolution features by convolution. Finally, a series of nearest neighbor classifiers are learned to hierarchically restore the missing parts of salient objects while refining their boundaries, yielding a more reliable final prediction. Comprehensive experiments demonstrate that this network performs favorably against state-of-the-art approaches on six datasets.

The aim of this paper is to introduce the notion of truthfulness in an influence based decision making model. An expert may submit his opinions truthfully or he may dismantle the original situation by undermining the actual opinion, such a decision maker is called an evasive decision maker or an almost truthful decision maker in this paper. It is assumed that experts in the panel are dignified members hence even though they are not habitual liars, they are either “almost truthful” or evasive. To measure their degree of truthfulness, we use the information provided by them in the form of preference relations. We use this information to state the foundation of influence model of evasive decision makers. Finally, a ranking method is proposed to find best possible solutions.

With the exponential growth of Internet technologies, digital information exchanged over the Internet is also significantly increased. In order to ensure the security of multimedia contents over the open natured Internet, data should be encrypted. In this paper, the quantum chaotic map is utilized for random vectors generation. Initial conditions for the chaos map are computed from a DNA (Deoxyribonucleic acid) sequence along with plaintext image through Secure Hash Algorithm-512 (SHA-512). The first two random vectors break the correlation among pixels of the original plaintext image via row and column permutation, respectively. For the diffusion characteristics, the permuted image is bitwise XORed with a random matrix generated through the third random vectors. The diffused image is divided into Least Significant Bit (LSB) and Most Significant Bits (MSBs) and Discrete Wavelet Transform (DWT) is applied to the carrier image. The HL and HH blocks of the carrier image are replaced with LSBs and MSBs of the diffused image for the generation of a visually encrypted image. The detailed theoretical analysis and experimental simulation of the designed scheme show that the proposed encryption algorithm is highly secured. Efficiency and robustness of the proposed visually image encryption scheme is also verified via a number of attack analyses, i.e., sensitivity attack analysis (> 99%), differential attack analysis (NPCR > 99, UACI > 33), brute force attack (almost 7.9892), statistical attack (correlation coefficient values are almost 0 or less than zero), noise tolerance, and cropping attack. Further security analyses such as encryption quality (I _D  ≅ 1564, D _H  = 3.000), homogeneity (0.3798), contrast (10.4820) and energy (0.0144) of the scheme are also evaluated.

Hesitant fuzzy sets (HFSs) play a dominant role in the decision making process. Different tools are developed to attract the decision makers (DMs) in making the effective decision, the hesitant fuzzy preference relation (HFPR) is one of the important implementation of them. Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In this paper, a hesitant fuzzy ranking (HFR) technique is established, constructed the hesitant fuzzy ranking from the HFPR in the group decision making situations. Secondly, a correlation between the alternatives is developed by using Spearman ranked correlation coefficient formula, which helps the DMs to identify the better alternative. The novelty of the proposed strategy is that it evades the need to compute the cooperative preference relations and approvals are generated for the individuals in their original domains.

 Aviation customer churn analysis is a difficult point, which has puzzled over airlines. The difficulties lie in the imbalance of customer churn data distribution and noisy data interference. Although some existing sampling techniques and ensemble models are good at dealing with class imbalance problem, noisy examples in dataset seriously affects the sampling quality and predictive accuracy of classifiers. Therefore, the purpose of our work is to effectively solve the problem of noise interference in imbalanced data classification and improve the effect of the ensemble classifier. In this paper, we propose a novel noise filtering algorithm that combined Tomek-link with distance weighted KNN (TWK), which can effectively filter the noise from both minority and majority class in the imbalanced dataset and prevent relative value samples from being rejected by mistake. We integrate TWK and feature sampling into EasyEnsemble to get a new ensemble model, named FSEE-TWK for short, for customer churn analysis. The introduction of feature sampling to FSEE-TWK accelerate the process of training and avoid model over-fitting. We obtained imbalanced customer data from a major Chinese airline to predict potential churn customers. We use F-Measure and G-Mean to evaluate the performance of the new ensemble model. The experimental results show that the proposed model can effectively improve the classification of datasets and significantly reduce the training time of the model.

Based on fuzzy inclusion order between L-subsets, stratified L-ordered uniform convergence spaces and stratified L-ordered limit spaces are introduced. It is shown that the resulting categories are all Cartesian closed topological categories. Also, the relationship among stratified L-ordered limit spaces, stratified L-ordered Cauchy spaces and stratified L-ordered uniform convergence spaces are investigated.

A novel Gini-Simpson (G-S) index based generalised grey target decision method for mixed attributes is put forward. The proposed method improves the G-S index and adopts it as the mixed attribute-based target centre distance from the viewpoint of measuring the difference of alternative index and target centre index. The core of this algorithm is to obtain the ratio of each alternative index to the target centre index. And the ratio is regarded as the pseudo probability, as makes a bridge between the alternative index and the target centre index. This method first transforms all indices into binary connection numbers and divides them into the deterministic terms and uncertain terms to constitute the two-tuple (determinacy, uncertainty) numbers. Then the target centre indices of two-tuple (determinacy, uncertainty) number are determined. Following this, the ratios of deterministic terms and uncertain terms of alternative indices to those of the target centre indices are calculated. Finally, the comprehensive weighted Gini-Simpson indices (CWGSIs) of all alternatives are obtained for decision-making with which the smaller value being the better. A case study illustrates the proposed approach.

This paper deals with uncertain linear systems called fully fuzzy linear systems (FFLSs) and dual FFLSs. The aim is to solve FFLSs and their duality. To get the purpose, a new approach based on the relative-distance-measure fuzzy interval arithmetic (RDM-FIA) is proposed. So far, many approaches based on fuzzy standard interval arithmetic (FSIA) have been suggested for solving FFLSs, and dual FFLSs. However, the suggested approaches suffer from some limitations, e.g. unnatural behavior in modeling (UBM) phenomenon. The limitations are regarded as either the sign of fuzzy numbers or the type of fuzzy numbers considered in systems. However, in this paper, the proposed approach does not have the limitations. Using two theorems, the general form of solutions of FFLSs and dual FFLSs are presented. By a corollary it was demonstrated that a dual FFLS can be regarded as an FFLS. In addition, restrictions associated to the FSIA-based approaches dealing with the FFLSs and dual FFLSs were pointed out. Furthermore, the effectiveness and efficiency of the proposed approach are demonstrated using some comparative examples.

The concept of pseudo MV-valuations is proposed in the paper, and some related characterizations of pseudo MV-valuations are investigated. The relationships between the pseudo MV-valuations of homomorphic and isomorphic MV-algebras and the relationships between their kernels are presented. We investigate several properties of pseudo MV-metrics induced by pseudo MV-valuations, and obtain that the product of two pseudo MV-metric spaces is a pseudo MV-metric space. Based on the introduced notion of pseudo continuous functions, we get that if a pseudo MV-valuation is contractive, then the binary operations on MV-algebras are pseudo continuous functions. Finally, we construct a congruence relation by using a pseudo MV-valuation, and study some properties of pseudo MV-valuations on quotient MV-algebras.

As a technique for granular computing, rough sets deal with the vagueness and granularity in information systems. Covering-based rough sets are natural extensions of the classical rough sets by relaxing the partitions to coverings and have been applied in many fields. However, many vital issues in covering-based rough sets, including attribute reduction, are NP-hard and therefore the algorithms for addressing them are usually greedy. Hence, it is necessary and helpful to generalize the covering-based rough sets from different viewpoints. In this paper, a new type of covering-based rough sets, named parametric covering-based rough sets, are proposed and some properties and applications of the parametric covering-based rough sets are investigated. First, a concept of inclusion degree is introduced into covering-based rough set theory to explore some properties of the parametric covering approximation space. Second, the parametric covering-based rough sets are established on the basis of inclusion degree. Moreover, some properties of the parametric covering-based rough sets are introduced. Third, it is found that the calculations of corresponding parametric covering-based lower and upper approximations can be converted into the operations of matrices, which makes the calculations convenient. Finally, a simple application of the parametric covering-based rough sets to network security is introduced.

This paper investigates intuitionistic fuzzy information aggration problem with the interrelationship among the input values and the “singular point” (i.e. the input value was either too large or too small) which canot be solved by most existing aggregation operators. To accomplish this, this paper combines the geometric Heronian mean (GHM) operator with the power geometric (PG) operator under intuitionistic fuzzy environment. Then, the intuitionistic fuzzy power GHM (IFPGHM) operator and the weighted intuitionistic fuzzy power GHM (WIFPGHM) operator are presented. The new operators capture not only the correlations between the input arguments but also the relative closeness of decision making information such that they can better solve the intuitionistic fuzzy information aggregation problem with diversified connections between arguments. The desirable properties of these new extensions of GHM operator and their special cases are investigated. Finally, based on the WIFPGHM operator, we present an approach to multiple attribute decision making and illustrate that approach with a practical example.

 Resource limitations in software projects rarely allow for the security requirements to be fully realized. As such, Prioritization and Selection (PAS) techniques are used to find an optimal subset of the requirements. Consequently, some of the security requirements will be ignored. But ignoring security requirements may (a) leave some of the security threats unattended and (b) negatively impact the effectiveness of the selected requirements. To mitigate this, we have proposed a fuzzy framework, referred to as Prioritization And Partial Selection (PAPS), that reduces the number of ignored security requirements by allowing for partial satisfaction of those requirements. We achieve this by relaxing the satisfaction conditions of security requirements, when tolerated, based on their priorities specified by a fuzzy inference system. Taking into account the partiality of security in PAPS mitigates the adverse impact of ignoring security requirements and enhances the accuracy of prioritization and selection. Our proposed framework is scalable to a large number of requirements.

 The main objective of this paper is to provide some characterizations of M-fuzzifying convex structures in terms of derived operators. We first introduce the notion of M-fuzzifying convexly derived operators, and then establish the one-to-one correspondence between M-fuzzifying convexly derived operators and M-fuzzifying convex structures. Additionally, it is proved that M-fuzzifying CP mappings can be expressed as formulas of derived sets. Finally, we introduce the notion of M-fuzzifying restricted convexly derived operators and prove that it is isomorphic to M-fuzzifying convex structures.

The present study is intended to provide a practical Decision Support System framework, based on Multi Agent System (MAS) and Intuitionistic Fuzzy Logic (IFL), useful for implementation in the healthcare area. The major objective consists in enabling the implementing of the conceived incremental project design, dubbed “smart healthcare”, in public or private healthcare centers (hospitals, polyclinics, etc.) through mobile cloud computing technology. In this regard, the present work is conceived to involve a thorough investigation and discussion of the IFL efficiency scope, as integrated into MAS architecture, for the purpose of detecting the patient’s health status in Intensive Care Units (ICUs). To this end, an implementation of the Intuitionistic Fuzzy Logic Decision Support System (IFLDSS), based on the Modified Early Warning Score (MEWS) standard, is carried out in the Tunisian Sfax city based ESSALEMA polyclinic. The proposed solution’s achieved results appears to reveal that the IFLDSS proves to display a commanding capacity in detecting uncertainty related to the ICU patients’ deteriorating cases. On comparing the IFL provided performance to that exhibited by the IFLDSS application, the findings appears to reveal well that the IFL MEWS appears to achieve remarkably higher accuracy scores than those provided by the MEWS standard.

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainty. In this work, new soft model, called the generalised multi-fuzzy bipolar soft model is proposed, and an algorithm based on this notion is presented. Some basic properties of this concept are studied and the related results are investigated. Finally, an application based on generalised multi-fuzzy soft sets in decision making is analyzed.

This paper focuses on extending and applying a fuzzy approach for utilization with the fully fuzzy multi-objective and multi-level integer quadratic programming (FFMMQP) problems. First, the decomposition technique is used to convert the fuzzy problem for each level into three crisp multi-objective integer quadratic (MQP) problems namely, Middle-MQP, Upper-MQP and Lower-MQP problem. Each crisp problem has its own variables. Furthermore, the functions of each problem have several quadratic functions. Then by considering the individual solution of each objective function, the middle, upper and lower membership functions are constructed. Second, the concept of the tolerance membership function and multi-objective optimization in the decomposition form is used to establish decomposed Tchebycheff problems to achieve the Pareto optimal fuzzy solution for the FFMMQP problems. An example is provided to prove the theoretical results.

This paper presents a new bi-level centralized resource allocation (CRA) model based on revenue efficiency which extends the classical revenue efficiency models to a more general case. In real world, there are large organizations like restaurant chains in which all the decision making units (DMUs) operate under the supervision of a central decision maker. In such intraorganizational scenario, the proposed bi-level model attempts to maximize the total revenue produced by all the DMUs and to minimize the reallocation cost in a hierarchical order under a centralized decision-making environment. Using the Karush-Kuhn-Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program with complementarity constraints (MPCC). According to optimization theory and some concepts of ordinary differential equations, a capable neural network is then developed to solve this one-level mathematical programming problem. Under proper assumptions and utilizing a suitable Lyapunov function, the proposed neural network is analyzed to be Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, some illustrative examples are elaborated to substantiate the applicability and effectiveness of the proposed approach.

 Quadratic programming is a special form of nonlinear programming and one of the most commonly used forms too. Linear programming is also none other than a particular case of quadratic programming. Ever-present impreciseness often makes way for natural inclination to fuzzy theory. In this paper, we intend to solve a quadratic programming problem (QPP) involving fuzzy parameters and fuzzy variables. We propose two approaches to solve such a QPP having not only fuzzy parameters in the objective function and constraints but fuzzy variables as well. This fully fuzzy QPP is eventually reduced to a crisp QPP and the solution is obtained in the form of fuzzy variables, first directly and later by applying Karush- Kuhn Tucker conditions. The proposed methods are also illustrated by some numerical examples.

 Social network analysis for multi agent based models can support deeper and empirically grounded understanding of the activities as well as agent’s roles in the system. An agent may store and share information of its environment with other agents of the system. Implementing a secure communication setup, in accordance with requested information is significant to select appropriate recipient. In such state of affairs cognitive phenomena like trust plays a vital role. Agents when converse based on trust establish emotional ties of varying strength in their social network. This paper presents a trust based fuzzy inference model in multi agent system by incorporating social relationships and contributes to analyze for cognitive agents for their roles as being influential, trustworthy and perilous. The model has also been implemented using Dempster Shafer Theory (DST) and the results are compared.

In this paper, the concept of quasi-coincidence of a bipolar fuzzy point within a bipolar fuzzy set is introduced. The notion of ∈-bipolar fuzzy soft set and q-bipolar fuzzy soft set is introduced based on a bipolar fuzzy set and characterizations for an ∈-bipolar fuzzy soft set and a q-bipolar fuzzy soft set to be bipolar fuzzy soft BCK/BCI-algebras are given. Also, the notion of (∈ , ∈ ∨ q)-bipolar fuzzy subalgebras and ideals are introduced and characterizes for an ∈-bipolar fuzzy soft set and q-bipolar fuzzy soft set to be a bipolar fuzzy soft BCK/BCI-algebras are established. Some characterization theorems of these (∈ , ∈ ∨ q)-bipolar fuzzy soft subalgebras and ideals are derived. The relationship among these (∈ , ∈ ∨ q)-bipolar fuzzy soft subalgebras and ideals are also considered.

The main aim of this paper is to evoke more attentions on the dual concepts of k-maxitive capacity and k-maxitive aggregation, called k-minitive capacity and k-minitive aggregation by convention. We point out that possibility and necessity capacities, and k-tolerant and k-intolerant capacities are special cases of k-maxitive and k-minitive capacities. We also discuss some properties of k-minitive aggregation dual to those of the k-maxitive aggregation functions. For the purport of advocating the application of k-minitive and k-maxitive capacities, we finally present the mixed integer programming based identification method and illustrate its steps and results through an example.

 Image denoising is a hot topic in many research fields, such as image processing and computer vision. With the development of deep learning, deep neural networks are widely used for image denoising and have achieved good effectiveness. Inspired by the characteristics of feed-forward denoising convolutional neural network (DnCNN) and biological neuron response, we propose a Symmetry-Rectifier Linear Unit (SyReLU) and further offer a corresponding SyReLU activation function, which has a better consistency with biological neuron characteristics in comparison with other activation functions, e.g. Rectifier Linear Unit (ReLU) and Leaky Rectifier Linear Unit(LReLU). Also, in order to denoise image, we use SyReLU activation function for residual learning of CNN (e.g. DnCNN). Specially, the experimental results indicate DnCNN with SyReLU can achieve better effectiveness than DnCNN with other activation functions (e.g.ReLU and LReLU) for image denosing on Set12 and BSD68 datasets. Briefly, the proposed method plays an important role in the development of activation function and is very useful in deep neural networks for image denosing.

Quality function deployment (QFD) is a systematic approach by which to incorporate the needs of customers within the process of product development. Unfortunately, semantic ambiguity pertaining to “hesitation” tends to undermine the effectiveness of QFD (both the conventional as well as fuzzy versions). In this study, we developed a novel QFD evaluation model referred to as intuitive fuzzy QFD in which an intuitive fuzzy analytic hierarchy process is implemented in conjunction with data envelopment analysis with the aim of deriving a more objective presentation of human thought processes when dealing with multiple-attribute problems within the context of group decision-making. The proposed model also takes into consideration cost limitations and difficulties associated with implementation. The practicality of the proposed model is demonstrated in a case study involving the design of machines for printing touch panels. In practice, this model can help the industrial develop and urge the promotion of design quality.

 Entropy has been used in many fields of computer vision, like image restoration, edge detection, pattern recognition, and as an evaluation method for image segmentation. The mean shift iterative algorithm (MSHi) was proposed in 2006, where the Shannon entropy was used as a stopping criterion. Later, it was introduced a theorem where this ensures, with a new stopping criterion, the convergence of the MSHi and determines what happens with the entropy at the limit of the segmentation process. The goal of this paper is carry out an analysis of the implications of this theorem and highlight the relation that were found from a physical point of view with image segmentation and the information theory. This last aspect being the novel part of this work.

 With the revolution of computing and biology technology, data sets containing information could be huge and complex that sometimes are difficult to handle. Dynamic computing is an efficient approach to solve some of the problems. Since neighborhood multigranulation rough sets(NMGRS) were proposed, few papers focused on how to calculate approximations in NMGRS and how to update them dynamically. Here we propose approaches for computing approximations in NMGRS and updating them dynamically. First, static approaches for computing approximations in NMGRS are proposed. Second, search region in data set for updating approximations in NMGRS is shrunk. Third, matrix-based approaches for updating approximations in NMGRS while decreasing or increasing neighborhood classes are proposed. Fourth, incremental algorithms for updating approximations in NMGRS while decreasing or increasing neighborhood classes are designed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

This paper considers networks as wireless sensor (hyper)networks and social (hyper)networks by single–valued neutrosophic (directed)(hyper)graphs.The notion of single–valued neutrosophic hypergraphs are extended to single–valuedneutrosophic directed hypergraphs and conversely. We derived single–valued neutrosophic digraphs from single–valued neutrosophic directed hypergraphs via a positive equivalence relation. It tries to use single–valued neutrosophic directed hypergraphs and positive equivalence relation to create the sensor clusters and to access to cluster heads in wireless sensor (hyper)networks. Finally, the concept of α-derivable single–valued neutrosophic digraph is considered as the energy-efficient protocol of wireless sensor networks and is applied this concept as a tool in wireless sensor (hyper)networks.

Operations for linguistic neutrosophic numbers (LNNs) have been receiving considerable attention. Existing LNNs operations are generally based upon Archimedean triangular norm and triangular conorm. However, the existing operations fail to consider the correlation among variables. Archimedean copulas and co-copulas can not only reveal the correlation among variables but also prevent information loss when they are used as aggregation functions in the aggregation process. Here, LNN operations are redefined based on Archimedean copulas and co-copulas. Meanwhile, some specific cases are discussed. Then, a linguistic neutrosophic improved generalized weighted Choquet Heronian mean operator is developed. According to the proposed operator, a multi-criteria decision-making method is proposed to tackle the selection problem of low-carbon suppliers. The influences of different generated functions and parameters are discussed, and the feasibility of the proposed method are validated through comparative analyses.

This paper proposes the concept of interval-valued average tree solution (“AT solution” for short) of graph cooperative games with interval-valued payoffs, and develop an effective and a direct simplified method for solving a subclass of interval-valued graph cooperative games. In this method, the interval-valued AT solution is proved to be a monotonic and non-decreasing function of coalitions’ values under specific condition. Hence, the lower and upper bounds of interval-valued AT solutions of graph cooperative games can be obtained directly by using the lower and upper bounds of the interval-valued coalitions’ payoffs, respectively. The proposed method gives better results than general interval subtraction and the partial subtraction operator methods. In addition, some important properties of the interval-valued AT solutions of interval-valued graph cooperative games are discussed. At last, the applicability and superiority of the proposed approach is demonstrated by comparing with other methods.

Driven by the entrepreneurial trend of mass entrepreneurship and innovation, venture capital(VC) has been widely concerned and valued by investors. There is no doubt that investment decision plays a critical role in venture capital, however, due to the complexity of the investment environment, it is often difficult for investors to make a definite judgement on an innovative solution. Consequently, to express more accurately the hesitation and ambiguity of investors in the decision-making process, this paper proposes the probabilistic linguistic hesitant fuzzy preference relation(PLHFPR) based on the probabilistic linguistic hesitant fuzzy set(PLHFS). Unlike hesitant fuzzy preference relation (HFPR), PLHFPR not only provides flexible linguistic expression for decision makers, but also gives the occurrence probability of each element in the PLHFPR. Considering that it is difficult for investors to give the exact probability of each element in the PLHFPR, a new probability calculation method is proposed based on the consistency analysis. What’s more, the convex consistency index(CCI) is defined to measure the consistency level of the PLHFPR by considering decision maker’s risk attitude. For the inconsistent PLHFPR, a weighted nonlinear programming model(WNPM) is constructed to derive an acceptable convex consistent PLHFPR and obtain the PLHFPR priority weight vector. Finally, an example about the venture capital is offered to verify the effectiveness of the proposed method.

Data Envelopment Analysis (DEA) is recognized as a robust analytical tool extensively utilized in measuring the relative efficiency of a group of decision-making units (DMUs) with multiple inputs and outputs. The DEA models require inputs and outputs equipped with precise information. However, in real-world situations, inputs and outputs may be unstable and complicated, thus unable to be accurately measured. This problem resulted in the investigation of uncertain DEA models. The RUSSELL model was studied in this paper in an uncertain environment where uncertain inputs and outputs were belief degree-based uncertainty, useful for the cases for which no historical information of an uncertain event is available. As the solution method, the uncertain RUSSELL model was converted to a crisp form using two approaches of expected value model and expected value and dependent chance-constrained model separately. Finally, an applied example regarding the Iranian banking system was presented to document the proposed models.

The normal parameter reduction is used as a useful approach to identify the irrelevant parameters in soft set-based decision making systems. It finds a subset with least number of parameters that preserve the original classification of the decision alternatives. A number of algorithms have been developed for the normal parameter reduction of soft set but the case of repeated columns (i.e., e _i  = e _j ) was only considered by Danjuma et al. In this study, first we address the limitations of the Danjuma et al.’s approach to normal parameter reduction of soft set. Then, we propose a new algorithm for normal parameter reduction of soft set which is free of all such limitations. Moreover, we compare the proposed algorithm with some of the existing algorithms of normal parameter reduction of soft set to show its efficiency. Finally, the application of the proposed algorithm is elaborated by a medical diagnostic problem.

Risk assessment is an important aspect of decision making while granting policy to an applicant. In the vast economy with enormous feature criteria for everyone, it is an ongoing challenge for the insurance companies to assess each applicant based on various factors to provide right policies on the basis of a risk score. We propose a method of ensemble learning as a solution to this problem where the predictions from pre-existing supervised learning algorithms can be used to enhance the accuracy of prediction. A real-world dataset having 128 attributes has been used to study the risk value associated with a policy applicant. Machine learning algorithms were applied to the dataset to predict the risk associated with the applicant. Two ensembles have been used for classification of risk level assigned to a person which further leveraged our approach to an optimized and efficient class of predictors namely ANN and gradient boosting algorithm XGBoost. As a result, we discovered that the XGBoost algorithm with optimized hyperparameters gave us the best results in terms of Quadratic Weighted Kappa Score. The proposed methodology outperforms other existing methodologies as discussed in the later sections of the paper.

As two important features of hesitant fuzzy linguistic term sets (HFLTSs), distance and similarity measures have been applied widely in many fields such as pattern recognition, decision making and prediction. Through analyzing the existing distance and similarity measures on HFLTSs, we find that they are not reasonable in some cases. Therefore, we first define the hesitance degree on HFLTSs to reflect the hesitant degree among several linguistic terms. On the basis of hesitance degree on HFLTSs, we develop several novel distance measures and further discuss their properties. Afterwards, several similarity measures based on hesitance degree are proposed and applied to pattern recognition. By comparing our novel proposed distance and similarity measures with the existing methods and giving an example of pattern recognition, we prove that our proposed distance and similarity measures are more reliable than the previous method in some cases.

Network providers and bandwidth brokers offer a variety of pricing policies based on differentiated quality-of-service (QoS) levels and volume discount schemes. In this paper, a cost minimization problem under various volume discount policies offered during the bandwidth allocation is formulated and solved via a heuristic algorithm. The proposed heuristic algorithm is based on fuzzy set theory. It has the capability of solving complex bandwidth provider selection and task allocation problems in telecommunications by considering a variety of volume discount policies offered by providers. The efficacy of the algorithm is tested under various scenarios to find the optimal strategies for firms and to explore the suitability of the proposed approach.

Collaborative filtering (CF) has achieved great performance in recommender system over past decades. CF-based methods firstly map users and items to latent factors which share the same latent space, and then use a linear function to predict user ratings on items, such as inner product or cosine distance. It only uses original latent feature, however feature interactions are usually helpful in enhancing recommendation performance. To tackle such issue, we used Factorization Machines (FM) to enhanced linear methods by incorporating the second-order feature interactions. In this paper, we propose a novel hybrid model, AutoFM, which combine Denoising Autoencoder (DAE) and FM together. AutoFM follows collaborative filtering method, it firstly uses DAE to map users and items to latent factor, then it uses FM calculating user ratings on items. To tackle the cold start problem, we also take as the input of FM user’s and item’s side information besides of latent factor. We conduct AutoFM on three real-world datasets, and the experiment results show that AutoFM consistently outperforms the state-of-the-art method.

Features of raw bearing vibration signals aren’t invariant with the change of rotating speed. As a result, determining the proper features is essential for the feature learning based intelligent fault diagnosis method for rolling element bearing with varying rotating speed. To address this issue, a convolutional neural network (CNN) based fault diagnosis approach is proposed. In the proposed method, envelope order spectra extracted from the raw vibration signals are used to provide abundant information about the fault characteristic orders, which are features invariant to the rotating speed. Subsequently, to extract these representative features automatically, a CNN model is constructed and employed, which avoid the manual feature selection. Finally, the type of bearing defects can be recognized successfully. In the experimental verification, the CNN is trained using a data set corresponds to one revolution per minute (RPM), while the data sets correspond to other RPMs are employed to verify the classification accuracy of the trained CNN, which can reflect the effectiveness of proposed method for bearing fault detection under different rotating speed. Experimental results show the satisfactory performance of fault-pattern recognition for the proposed method. When compared with some other approaches using intelligence-based fault diagnosis method, the results show the superiority of the proposed method.

Measuring the similarity between images is an essential problem in various image processing and pattern recognition applications. In pattern recognition problems, it is indispensable to give formulas for calculating similarity between different patterns. But it is very difficult to find a certain measure that can be successfully applied to all kinds of pattern recognition problems. Intuitionistic fuzzy sets have been successfully applied to various areas such as pattern recognition and medical diagnostics. In intuitionistic fuzzy sets theory, the calculation of the similarity between intuitionistic fuzzy sets is a significant technique for distinguishing the similarity degree between intuitionistic fuzzy sets. The existing similarity measures almost are obtained in the sense of distance. In this paper, we present a novel way to obtain the similarity measure between intuitionistic fuzzy sets from a new perspective. Our main purpose is to show that according to the membership and non-membership functions of intuitionistic fuzzy sets, a triangular norm can induce an inclusion degree. Using this triangular norm and the induced inclusion degree, a similarity measure of intuitionistic fuzzy sets can be obtained. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy sets. As the applications of similarity degree proposed in this paper, we first present an intuitionistic fuzzy clustering algorithm based on similarity degree. Then, the similarity degree proposed in this paper is applied to pattern recognition. At the same time, the numerical examples are employed to illustrate the effectiveness of proposed method.

Formal concept analysis, originally proposed by Wille, is a mathematical tool to analyse and represent data in the form of complete formal context. However, in situations with incomplete information, one only has partial knowledge about a concept, recently, a common conceptual framework of the notions of interval sets and incomplete formal contexts for representing partially-known concepts were presented. In this study, we examine and reinterpret the existing studies on partially known concepts by means of three-valued logics. By treating an incomplete formal context as a three-valued formal context and considering the one-to-one correspondence between interval sets and three-valued mappings, we investigate the condition under which the four types of partially known concepts can be generated by using three-valued implication operators. Moreover, we also evaluate the role of three-valued logic in characterizing attribute implications. A sufficient and necessary condition for computing the true value of an implication correctly in the sense of Kriple semantics is provided.