Integrated model of assisted parking system and performance evaluation with entropy weight extended analytic hierarchy process and two-tuple linguistic information

Abstract

Evaluating comprehensive performance of assisted parking system has been a very important issue for car companies for years, because the overall performance of assisted parking system directly influences car intellectualization and customers’ degree of satisfaction. Therefore, this article proposes two-tuple linguistic analytic hierarchy process to evaluate assisted parking system so as to avoid information loss during the processes of evaluation integration. The performance evaluation attributes for assisted parking system are established initially. Subsequently, the information entropy theory is proposed to improve the evaluation attribute weight determined by analytic hierarchy process for the influencing factors of the randomness in parking test process. Furthermore, the evaluation attribute measure values of comprehensive performance are calculated and the assisted parking system evaluation results are obtained with ordered weighted averaging operator. Finally, numerical examples of vehicle types equipped with eight different assisted parking systems and computational results are presented.

Keywords

Assisted parking system analytical hierarchy process two-tuple information entropy evaluation method

Introduction

With the rapid growth of car ownership, “parking difficulty” problem in modern cities is more and more notable. Parking operation in parking areas near crowded and narrow urban roads and community roads is not easy for many drivers. Therefore, assisted parking driving technology has become one of the research hotspots in car engineering field. The car makers paying much attention to assisted parking system successively launch their own assisted parking driving system.^1,2

In recent years, the advanced technologies relating to parking drew much attention from people and assisted parking driving technology has gradually won people’s favor. The advanced assisted parking technology is leading to subtle changes in the external environment of market. The investigation results from foreign car consulting companies show that customers begin to raise higher requirements for car intellectualization and prefer to spend more money on the cars with assisted parking system.^3,4 The overall performance of assisted parking system directly influences customers’ degree of satisfaction, and the assessment of the overall performance is a multi-level, multi-factor, and multi-objective comprehensive result;^5,6 the overall performance of assisted parking system is decided by many factors and the results conforming to the reality can be obtained only by analyzing comprehensively different factors.⁷ Therefore, the influencing factors should be summarized by levels through the comprehensive analysis of the existing assisted parking systems and combined with mathematical methods to determine comprehensive evaluation results. An effective scientific basis is needed for the improvement of the overall performance of new assisted parking system.^8–10 Now, there is still a blank in the research on the comprehensive evaluation methods of the overall performance of assisted parking system.

Hierarchy analysis method is currently a relatively mature weight calculation method, applied in many fields. It was put forward by American operational research expert TL Saaty¹¹ in early 1980s. It regards a complex multi-target decision-making problem as a system and divides one big target into many small targets or principles to divide attributes into many levels and calculate single hierarchical arrangement and general ranking by qualitative fuzzy quantifying method.¹² But traditional hierarchy analysis method has obvious disadvantages, namely, its measurement scaling method is a deterministic method having not taken the thinking fuzziness of evaluation personnel into account, which will influence the accuracy of the evaluation results.¹³

The expression of traditional fuzzy linguistic preference is divided into fuzzy number method and language scaling method, both of which have certain limitations, namely, the group evaluation information obtained by collecting individual evaluation information generally. But they cannot be expressed by the single linguistic phrase obtained from the predefined semantic evaluation and need an approximate process, which leads to the loss of information and the inaccuracy of the collected results. For that, Spanish scholars Herrera and Martinez¹⁴ raised binary language analysis method relating to language information collection in 2000 to well overcome the disadvantages of previous research methods. The method regards language phrases as the continuous variables within its domain of definition and can use the binary form of one phrase and the value of one real number to express all information obtained after language evaluation information integrity, which effectively avoids the information loss and distortion happening in language evaluation information aggregation and calculation. It is superior to other language information processing methods in calculation accuracy and reliability.^15,16 According to the above analysis, the comparison of fuzzy number, language scaling, two-tuple linguistic in expression accuracy, calculation simplicity, and information loss is shown in Table 1.^17,18

Table 1.

Representation comparison of different fuzzy linguistic preferences.

Expression method		Expression accuracy	Calculation simplicity	Information loss
Fuzzy number	Triangular fuzzy number	Good	Difficult	Loss
Fuzzy number	Trapezoid fuzzy number	Good	Difficult	Loss
Language scaling		Good	Simple	Loss
Two-tuple linguistic		Best	Simple	Little loss

Because the weight coefficient determined by hierarchy analysis method has not considered the randomness in parking experiment process, the article raises an information entropy–based method to improve the weight coefficient determined by hierarchy analysis method. Entropy was first put forward by Shannon in 1948, generally called information entropy or Shannon entropy. Information entropy is an uncertain measurement.¹⁹ The bigger the information, the higher the uncertainty of information and the lower the usefulness value; otherwise, the smaller the information entropy, the lower the uncertainty and the higher the usefulness value of information. Information entropy has been applied to almost all subjects and plays an important role in modern power system and ergodic theory.^20,21 Its application in natural science,²² social science,²³ and management science becomes more and more mature.

The article gives subjective assessment (qualitative) and objective assessment (quantitative) to the assisted parking systems of different vehicle types according to many drivers’ experiment evaluation and builds structural models of analysis methods and judgment matrix. In order to overcome the disadvantages of subjective assessment, it puts forward the two-tuple linguistic theory-based subjective assessment method. Given the randomness of the parking experiment results, it adopts information entropy theory to determine the weight of attributes. The measure values of attributes are obtained by calculating the binary semantic expert evaluation values. Then, the assessment results of the performance of assisted parking system of different vehicle types are obtained by calculating the measure values of attributes with ordered weighted averaging (OWA) operator. The differences in the performance of the assisted parking systems of different vehicle types are differentiated by analyzing the assessment results to provide a reference basis for improving the performance of different assisted parking systems or adjusting technical scheme.

Preliminaries

Basic principles and prospect of assisted parking system

The operating principle of assisted parking system is to measure the distance and angle between car and neighboring barriers with vehicular distance detection equipment and then to calculate the procedures of parking with vehicular controller which will be combined with car speed to change the driving direction of car.²⁴ Drivers only need to control the driving speed of cars, as shown in Figure 1. Assisted parking system is the current research hotspot in car driving-assisted technology field and involves the knowledge about electromagnetism, environment-aware sensor, signal processing, information fusion, model identification, automatic control and electric power steering direction, and automotive electronics.²⁵ With the constant improvement of popularity rate of car, there is less and less space for parking on urban roads, but assisted parking system provides a great help for solving the parking in a narrow space, so it has a wide application space in the future.²⁶ Refer to Figures 2 and 3 for the schematic diagrams of parking route design and parking effects.

Figure 1.

Assisted parking system work process.

Figure 2.

Schematic of the path planning.

Figure 3.

Schematic of parking evaluating results.

Definition and computing of two-tuple linguistics information

Two-tuple linguistics adopts a binary group $(s_{i}, a_{i})$ to express language assessment information.²⁷ Among these, $s_{i}$ is the ith element in the predefined language assessment set and represents the language phrase in initial language assessment set most approximate to language assessment results; $a_{i}$ is the symbol transfer value representing the difference between the assessment results and $s_{i}$ , and $a_{i} \in [- 0.5, 0.5]$ .

Definition 1

Let $s_{i} \in S$ be a linguistic label. Then, the function $θ$ used to obtain the corresponding two-tuple linguistic information of $s_{i}$ is defined as

\begin{matrix} θ : S \to S \times [- 0.5, 0.5] \\ θ (s_{i}) = (s_{i}, 0), s_{i} \in S \end{matrix}

(1)

Definition 2

Let $S = {s_{1}, s_{2}, \dots, s_{t}}$ be a linguistic term set and $β \in [1, t]$ is a number value representing the aggregation result of linguistic symbolic. Then the function $Δ$ used to obtain the two-tuple linguistic information equivalent to $β$ is defined as

\begin{matrix} Δ : [1, t] \to S \times [- 0.5, 0.5) \\ Δ (β) = {\begin{matrix} s_{i}, i = round (β) \\ α = β - i, α \in [- 0.5, 0.5) \end{matrix} \end{matrix}

(2)

where $round (\cdot)$ is the usual round operation, $s_{i}$ has the closest attribute label to $β$ , and $α$ is the value of the symbolic translation.

Definition 3

Let $S = {s_{1}, s_{2}, \dots, s_{t}}$ be a linguistic term set and $(s_{i}, α_{i})$ be a two-tuple. Function $Δ^{- 1}$ has always be defined, such that from a two-tuple $(s_{i}, α_{i})$ it returns its equivalent numerical value $β \in [1, t] \subset R$ . Then the function $Δ^{- 1}$ is defined as

\begin{matrix} Δ^{- 1} : S \times [- 0.5, 0.5) \to [1, t] \\ Δ^{- 1} (s_{i}, α) = i + α = β \end{matrix}

(3)

Definition 4

Let $(s_{k}, a_{k})$ and $(s_{l}, a_{l})$ be two two-tuple; they should have the following properties

If k < l, then $(s_{k}, a_{k})$ is smaller than $(s_{l}, a_{l})$

If k = l, then,

if $a_{k} = a_{l}$ , then $(s_{k}, a_{k})$ , $(s_{l}, a_{l})$ represent the same information

if $a_{k} < a_{l}$ , then $(s_{k}, a_{k})$ is smaller than $(s_{l}, a_{l})$

if $a_{k} > a_{l}$ , then $(s_{k}, a_{k})$ is bigger than $(s_{l}, a_{l})$

Definition 5

Assume ${(s_{1}, a_{1}), (s_{2}, a_{2}), \dots (s_{n}, a_{n})}$ is a group of binary semantic information set and $ω = (ω_{1}, ω_{2}, \dots ω_{n})^{T}$ is its corresponding weight of real number, then the two-tuple weighted averaging (T-WA) operator is

\begin{matrix} (\tilde{s}, \tilde{a}) = Δ (\sum_{i = 1}^{n} Δ^{- 1} (s_{k}, a_{k}) \times ω_{i}) \\ \tilde{s} \in T, \tilde{a} \in [- 0.5, 0.5) \end{matrix}

(4)

Definition 6

Assume ${(s_{1}, a_{1}), (s_{2}, a_{2}), \dots (s_{n}, a_{n})}$ is a group of binary semantic information set, then the two-tuple ordered weighted averaging (T-OWA) operator is

\begin{matrix} (\hat{s}, \hat{a}) = Δ (\sum_{i = 1}^{n} b_{i} v_{i}) \\ \hat{s} \in T, \hat{a} \in [- 0.5, 0.5) \end{matrix}

(5)

Among these, $b_{i}$ is an element in $B = (b_{1}, b_{2}, \dots, b_{n})^{T}$ representing the ith element in ${Δ^{- 1} (s_{i}, a_{i}) | i = 1, 2, \dots, n}$ in descending order; $v_{i}$ is an element in vector $V = (v_{1}, v_{2}, \dots, v_{n})^{T}$ representing the position weight vector relating to OWA operator,²⁸ and the value of $v_{i}$ is determined by Q

v_{i} = Q (\frac{i}{n}) - Q (\frac{i - 1}{n}), i = (1, 2, \dots, n)

(6)

Among these, $v_{i} \in [0, 1]$ and $\sum_{i = 1}^{n} v_{i} = 1$ ; operator for fuzziness Q is obtained from the following equation

Q (r) = {\begin{matrix} 0, r < a \\ \frac{r - a}{b - a}, a \leq r \leq b \\ 1, r > b \end{matrix}

(7)

Among these, in different cases, the corresponding parameters of the operator $Q (r)$ for fuzziness are, respectively, (0, 0.5), (0.3, 0.8), and (0.5, 1).

Definition 7

Assume ${(s_{1}, a_{1}), (s_{2}, a_{2}), \dots (s_{n}, a_{n})}$ is the set of a group of two-tuple linguistic information, then the two-tuple ordered weighted geometric (T-OWG) operator²⁹ is

\begin{matrix} (\hat{s}, \hat{a}) = Δ (Π_{i = 1}^{n} {b_{i}}^{v_{i}}) \\ \hat{s} \in T, \hat{a} \in [- 0.5, 0.5) \end{matrix}

(8)

Among these, $b_{i}$ is an element in vector $B = (b_{1}, b_{2}, \dots, b_{n})^{T}$ representing the ith element in ${Δ^{- 1} (s_{i}, a_{i}) | i = 1, 2, \dots, n}$ in descending order; $v_{i}$ is an element in vector $V = (v_{1}, v_{2}, \dots, v_{n})^{T}$ representing the position weight vector relating to OWG operator; the value of $v_{i}$ is determined by the operator Q for fuzziness (formulas (6) and (7)).

Evaluation model of assisted parking system and methodologies for computing

Building evaluation model of assisted parking system

According to experimental experience from plenty of assisted parking real vehicle tests, as well as considering V-Charge project (Automated Valet Parking and Charging for e-Mobility Collaborative Project) and ASSESS project (Assessment of Integrated Vehicle Safety Systems for improved vehicle safety), it puts forward selecting 18 representative attributes (secondary attributes) from initial search performance A1, parking processing performance A2, parking effects A3, and drivers’ feeling in parking A4 (primary attributes) to build comprehensive performance evaluation attribute system of assisted parking system, as shown in Figure 4.

Figure 4.

Evaluation attribute system of assisted parking system comprehensive performance.

Some supplements for V-Charge project are given as follows. The objective of this project is to develop a smart car system that allows for autonomous driving in designated areas (e.g. valet parking, park and ride) and can offer advanced driver support in urban environments. The final goal in 4 years is the demonstration and implementation of a fully operational future car system including autonomous local transportation, valet parking, and battery charging on the campus of ETH Zurich and TU Braunschweig. The envisioned key contribution is the development of safe and fully autonomous driving in city-like environments using only low-cost Global Positioning System (GPS), camera images, and ultrasonic sensors.

Similarly, some details about ASSESS project are given as follows. ASSESS mobilizes the European research community and car industry to develop a relevant set of test and assessment methods applicable to a wide range of integrated vehicle safety systems including parking system. Methods will be developed for driver behavioral aspects, pre crash sensing performance, and crash performance under conditions influenced by pre crash driver and vehicle actions. The gained know-how will be implemented in proposals for test and assessment procedures that will be evaluated on the basis of actual systems currently offered to the market.

Methodologies for computing

Step 1. Experiment of assisted parking systems with subjective assessment (qualitative) and objective assessment (quantitative). Three experienced car testers conduct subjective and objective assessment on eight vehicle types with different assisted parking systems. The assessment data are obtained by E1–E3 tester. Among these, B1–B2, B7–B8, and B15–B18 belong to subjective qualitative assessment attributes, in two-tuple linguistic form S = {s₀ = extremely bad, s₁ = very bad, s₂ = worse, s₃ = bad, s₄ = common, s₅ = good, s₆ = better, s₇ = very good, s₈ = extremely good}; B3–B6 and B9–B14 belong to objective quantitative assessment attributes and they are provided by actual experiment data; B3 and B10–B14 are negative attributes, namely, the bigger the data, the worse the attribute, and other attributes are positive; the data of B11 and B12 are obtained after calculation, namely, the absolute value of the differences between them and standard value 80 cm.

Step 1.1. Attribute standardization. Attributes according to usefulness coefficients. If d_i is adopted, the specific forms of d_i = d_i(x_i), i = 1, 2, 3,…, m are various. For different attributes, the following two linear expressions are provided.

Positive attributes

d_{i} = d_{i} (x_{i}) = {\begin{matrix} 1, x_{i} \geq x_{b} \\ \frac{x_{i} - x_{a}}{x_{b} - x_{a}}, x_{i} \in [x_{a}, x_{b}] \\ 0, x_{i} \leq x_{a} \end{matrix}

(9)

Negative attributes

d_{i} = d_{i} (x_{i}) = {\begin{matrix} 1, x_{i} \leq x_{a} \\ \frac{x_{b} - x_{i}}{x_{b} - x_{a}}, x_{i} \in [x_{a}, x_{b}] \\ 0, x_{i} \geq x_{b} \end{matrix}

(10)

Step 2. The determination of weighted coefficient of judgment attributes.³⁰

Step 2.1. The establishment of judgment matrix using analytic hierarchy process (AHP). According to the literatures and specifications about parking, analysis of parking test results and engineering analogy analysis, determine the importance of the any two attributes and elaborate on the building method of judgment matrix to it. The judgment matrix of pairwise comparison according to the scaling meaning is given in Table 2.

Step 2.2. Judgment matrix consistency examination and examination results. In the calculation of weight coefficients, the consistency of judgment matrix A needs to be examined with the specific methods as follows:

Calculate the maximum characteristic value of judgment matrix

λ_{max} = \frac{1}{m} \sum_{i = 1}^{m} \frac{{(\tilde{A} W)}_{i}}{ω_{i}}

(11)

Among these, $ω_{i} = \partial_{i} / \sum_{k = 1}^{m} \partial_{k}, (i = 1, 2, \dots, m), \partial_{i} = \sum_{i = 1}^{m} q_{ij}, (i = 1, 2, \dots, m)$ , $q_{ij} = {\tilde{a}}_{ij} / \sum_{k = 1}^{m} {\tilde{a}}_{kj}, (i, j = 1, 2, \dots, m)$ .

Calculate consistency attribute

CI = \frac{λ_{max} - m}{m - 1}

(12)

Random consistent attributes RI is obtained from sheet, as shown in Table 3.

Calculate consistency rate $CR = CI / RI$ with the calculation results as follows. When $CR \leq 0.1$ , the judgment matrix and weights of attributes are accepted. Otherwise, experts should be asked to rejudge.

Table 2.

Judgment matrix scale and its meaning.

Scaling	Meaning
1	Each factor has equal importance
3	First factor is more important than the second factor
5	First factor is very important with respect to the second factor
7	First factor is exactly very important with respect to the second factor
9	First factor is absolutely very important with respect to the second factor
2, 4, 6, 8	Intermediate values
Reciprocal	Judgment value for the comparison of i and j is b_ij; importance ratio of i and j is b_ji = 1/b_ij

Table 3.

Mean random consistency attribute table.

Order of matrix	1	2	3	4	5	6	7	8	9
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46

The steps of AHP approach for assisted parking system are shown in Figure 5.

Figure 5.

AHP approach for assisted parking system.

Step 2.3. The determination and improvement of weight. Because the weight coefficient determined by hierarchy analysis method has not considered the randomness in parking experiment process, the article raises an information entropy–based method to improve the weight coefficient determined by hierarchy analysis method.

Assume there is m assisted parking system awaiting to be assessed and the overall performance of each assisted parking system is assessed by n factors, the weight of each factor can be obtained by calculating the information entropy of each factor to evaluate the overall performance of each assisted parking system with the specific procedures as follows:³¹

Normalize $x_{ij}$ and calculate the proportion $P_{ij}$ of the ith scheme of the jth attribute

P_{ij} = \frac{x_{ij}}{\sum_{i = 1}^{m} x_{ij}} (i = 1, 2, \dots, m; j = 1, 2, \dots, n)

(13)

Calculate the entropy $h_{i}$ of the ith scheme

\begin{array}{l} h_{i} = - K -_{j = 1}^{n} P_{i j} \ln P_{i j} (i = 1, 2, \dots, m) \\ K = \frac{1}{\ln m} \geq 0, h_{j} \geq 0 \end{array}

(14)

The information usefulness value of one attribute depends on the difference between the information entropy $h_{i}$ of the attribute and 1, namely

D_{j} = 1 - h_{j}

The higher the usefulness value of one attribute, the greater its importance for evaluation and the bigger the attribute weight. The entropy weight of jth attribute is

ω_{j} = \frac{D_{j}}{\sum_{j = 1}^{n} D_{j}}

(15)

Finally, the value of comprehensive weight is obtained by calculating the entropy weights of attributes and combining the weight determined by AHP. Let $ω_{AH P_{j}} = ω_{i}$ . The comprehensive weight $ω'_{j}$ is calculated as follows

ω'_{j} = \frac{ω_{AH P_{j}} \times ω_{j}}{\sum_{j = 1}^{n} ω_{AH P_{j}} \times ω_{j}}

(16)

Step 3. The evaluation results and analysis of the overall performance of assisted parking system.

Step 3.1. Building two-tuple linguistics-based measure model. First, build two-tuple linguistic matrix and transform all quantitative data in original assessment data into two-tuple linguistic form. Conduct same processing to the original assessment data obtained from E2 and E3 assisted parking system testers. The calculation formula is as follows

(s'_{i}, α'_{i}) = \frac{s_{max}}{max {\frac{x_{ij}}{\sum_{i = 1}^{n} x_{ij}}}} \times \frac{x_{ij}}{\sum_{i = 1}^{n} x_{ij}}

(17)

Among these, $s_{max} = max {Δ^{- 1} (s_{i}, α)} = 8$ .

Step 3.2. Calculate the measure value. Calculate the measure value of the primary attributes provided by each tester. Calculate the corresponding measure value according to formula (4). Among these, $Δ^{- 1} (s_{k}, a_{k})$ is obtained by calculating according to formula (3).

Step 3.3. Calculate the comprehensive measure values of A-H.

Determine position weight vector. The article chooses (a, b) = (0.3, 0.8) as the corresponding fuzzy quantifier parameter. The number of testers is 3, namely, m = 3. The position weight vector relating to OWA operator can be figured out according to formulas (6) and (7), namely

V = (v_{1}, v_{2}, v_{3})^{T} = (0.0667, 0.667, 0.2667)^{T}

Calculate comprehensive measure value. Let i = 1; this moment, $Δ^{- 1} (s_{ki}, a_{ki}) = Δ^{- 1} (s_{k 1}, a_{k 1})$ means measure value of A1. Rank $Δ^{- 1} (s_{k 1}, a_{k 1})$ in descending order and get $B = (b_{1}, b_{2}, b_{3})^{T}$ . Then put $b_{i}$ and corresponding $v_{i}$ into formula (5) and get the comprehensive measure value of the overall performance of assisted parking system of vehicle type A. Similarly, the comprehensive measure value of vehicle type B-H can be obtained.

Calculating the overall scores of different vehicle types. Calculate the overall scores according to

(\tilde{s}, \tilde{a})_{score} = Δ (\sum_{i = 1}^{4} Δ^{- 1} (s_{ki}, a_{ki}) \times {ω ″}_{i}) .

Figure 6 shows the steps of the proposed approach under three main sections (i.e. AHP approach, entropy approach, and T-OWA approach).

Figure 6.

Entropy weight extended AHP with two-tuple approach for assisted parking system.

Case study and results’ analysis

In this case, the proposed method is applied to evaluate the comprehensive performance of different assisted parking systems. Because the different types of vehicles directly affect the overall performance of assisted parking. For example, different kinds and models of sensors used to detect parking lot will affect the performance of searching parking lot (A1); parking controller about the path planning control strategy will affect the performance in parking procedure (A2); vehicle size will absolutely influence parking result (A3); vehicle different engines will affect drivers’ feelings in parking (A4). Therefore, in this article, the above factors are considered. Different parameters and vehicle types are selected in car market. The corresponding relations between vehicle type A-H and actual vehicle types are shown in Table 4. The actual test of assisted parking system is shown in Figure 7.

Table 4.

Actual corresponding vehicle types.

Vehicle types	Vehicle type A	Vehicle type B	Vehicle type C	Vehicle type D
Actual corresponding vehicle types	Volkswagen Tiguan 2.0TSI	Lexus LS460L	HaiMa Family 1.5T	Ford Kuga 2.0T
Vehicle types	Vehicle type E	Vehicle type F	Vehicle type G	Vehicle type H
Actual corresponding vehicle types	Hyundai Santa 2.0T	Audi A7 40TDSI	BYD Surui 1.5L	Peugeot 408 1.6T

Figure 7.

Actual test of assisted parking system.

Step 1. The assessment data are obtained by E1–E3 tester, make data dimensionless shown in Tables 5 –7.

Step 1.1.Quantitative attributes units are shown in Table 8.

Step 2. The determination of weight coefficient of judgment attributes.

Step 2.1. The establishment of judgment matrix using AHP. Judgment matrixes are shown in Tables 9 –13.

Step 2.2. Judgment matrix consistency examination and examination results

Table 5.

Raw data of E1 test member for evaluating eight vehicle types.

	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11	B12	B13	B14	B15	B16	B17	B18
A	(s₇, 0)	(s₆, 0)	0.01	4	25	90	(s₆, 0)	(s₆, 0)	15	0	5	5	5	5	(s₆, 0)	(s₇, 0)	(s₈, 0)	(s₆, 0)
B	(s₅, 0)	(s₅, 0)	0.03	3.2	20	85	(s₇, 0)	(s₃, 0)	10	2	20	20	7	10	(s₅, 0)	(s₄, 0)	(s₇, 0)	(s₇, 0)
C	(s₅, 0)	(s₆, 0)	0.01	4.5	25	95	(s₈, 0)	(s₇, 0)	13	0	15	15	3	5	(s₇, 0)	(s₈, 0)	(s₇, 0)	(s₈, 0)
D	(s₆, 0)	(s₁, 0)	0.02	4	25	90	(s₇, 0)	(s₆, 0)	15	1	10	10	5	10	(s₆, 0)	(s₇, 0)	(s₇, 0)	(s₇, 0)
E	(s₁, 0)	(s₅, 0)	0.01	3.5	20	85	(s₆, 0)	(s₇, 0)	10	1	7	7	4	0	(s₆, 0)	(s₆, 0)	(s₇, 0)	(s₇, 0)
F	(s₆, 0)	(s₈, 0)	0.01	5	30	95	(s₇, 0)	(s₈,−0.2)	15	0	0	0	3	0	(s₇, 0)	(s₈, 0)	(s₈, 0)	(s₈, −0.2)
G	(s₇, 0)	(s₇, 0)	0.05	3.5	20	85	(s₅, 0)	(s₆, 0)	10	2	30	30	10	10	(s₆, 0)	(s₅, 0)	(s₅, 0)	(s₅, 0)
H	(s₅, 0)	(s₇, 0)	0.04	3.2	20	80	(s₅, 0)	(s₆, 0)	10	2	40	40	15	10	(s₅, 0)	(s₆, 0)	(s₆, 0)	(s₅, 0)

Table 6.

Raw data of E2 test member for evaluating eight vehicle types.

	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11	B12	B13	B14	B15	B16	B17	B18
A	(s₇, 0)	(s₇, 0)	0.01	4	25	90	(s₇, 0)	(s₄, 0)	15	0	5	5	5	5	(s₅, 0)	(s₆, 0)	(s₇, 0)	(s₆, 0.4)
B	(s₆, 0)	(s₅, 0)	0.03	3.2	20	85	(s₆, 0)	(s₅, 0)	10	2	20	20	7	10	(s₆, 0.2)	(s₅, −0.3)	(s₆, 0.2)	(s₆, 0.1)
C	(s₄, 0)	(s₅, 0)	0.01	4.5	25	95	(s₆, 0)	(s₄, 0.2)	13	0	15	15	3	5	(s₆, −0.2)	(s₆, −0.3)	(s₆, −0.2)	(s₇, −0.2)
D	(s₇, 0)	(s₂, 0)	0.02	4	25	90	(s₇, 0.2)	(s₅, 0.3)	15	1	10	10	5	10	(s₅, 0.2)	(s₅, 0.3)	(s₅, 0.4)	(s₆, 0.2)
E	(s₂, 0)	(s₆, 0)	0.01	3.5	20	85	(s₆, 0.4)	(s₆, 0.2)	10	1	7	7	4	0	(s₆, 0.1)	(s₆, 0.4)	(s₆, −0.3)	(s₆, −0.3)
F	(s₈, 0)	(s₈, 0)	0.01	5	30	95	(s₈, 0)	(s₇, 0.3)	15	0	0	0	3	0	(s₇, 0.3)	(s₇, 0.1)	(s₇, 0.1)	(s₈, −0.4)
G	(s₄, 0)	(s₅, 0)	0.05	3.5	20	85	(s₄, 0)	(s₅, −0.3)	10	2	30	30	10	10	(s₅, 0.3)	(s₆, −0.4)	(s₄, 0.4)	(s₄, 0.1)
H	(s₆, 0)	(s₆, 0)	0.04	3.2	20	80	(s₆, 0)	(s₅, 0.3)	10	2	40	40	15	10	(s₄, 0.4)	(s₅, 0.2)	(s₅, 0.3)	(s₅, 0)

Table 7.

Raw data of E3 test member for evaluating eight vehicle types.

	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11	B12	B13	B14	B15	B16	B17	B18
A	(s₆, 0.2)	(s₅, 0.3)	0.01	4	25	90	(s₆, 0)	(s₅, 0)	15	0	5	5	5	5	(s₆, 0.4)	(s₇, −0.4)	(s₇, 0.1)	(s₅, 0.3)
B	(s₅, 0.1)	(s₅, 0.4)	0.03	3.2	20	85	(s₅, 0.4)	(s₆, −0.4)	10	2	20	20	7	10	(s₅, 0.3)	(s₅, −0.2)	(s₇, 0)	(s₇, −0.2)
C	(s₄, −0.2)	(s₆, −0.1)	0.01	4.5	25	95	(s₆, 0.3)	(s₅, 0.3)	13	0	15	15	3	5	(s₆, 0.2)	(s₆, 0.4)	(s₆, 0.2)	(s₇, 0.1)
D	(s₆, 0.3)	(s₁, 0.4)	0.02	4	25	90	(s₇, −0.3)	(s₅, 0.2)	15	1	10	10	5	10	(s₅, 0.1)	(s₇, −0.3)	(s₇, 0.4)	(s₇, −0.3)
E	(s₁, 0.3)	(s₅, 0.4)	0.01	3.5	20	85	(s₆, 0)	(s₆, 0.4)	10	1	7	7	4	0	(s₅, 0)	(s₅, 0)	(s₇, 0)	(s₆, 0)
F	(s₇, 0.2)	(s₇, 0.4)	0.01	5	30	95	(s₇, −0.3)	(s₇, 0.4)	15	0	0	0	3	0	(s₇, 0.2)	(s₈, 0)	(s₇, 0.1)	(s₇, 0)
G	(s₅, 0.2)	(s₆, 0.3)	0.05	3.5	20	85	(s₅, 0.4)	(s₅, 0.1)	10	2	30	30	10	10	(s₅, −0.3)	(s₅, 0.3)	(s₅, 0)	(s₆, 0.2)
H	(s₅, −0.4)	(s₅, 0.2)	0.04	3.2	20	80	(s₆, 0.2)	(s₆, −0.2)	10	2	40	40	15	10	(s₄, 0.2)	(s₆, 0)	(s₆, 0.2)	(s₅, −0.2)

Table 8.

Quantitative attributes and units.

Quantitative attributes	B3(-)	B4	B5	B6	B9	B10(-)	B11(-)	B12(-)	B13(-)	B14(-)
Units	m	m	km/h	%	km/h	–	cm	cm	Cm	°

Attributes with “(-)” mean cost ones.

Table 9.

Judgment matrix of assisted parking system overall performance.

	A1	A2	A3	A4
A1	1	1/2	1/2	3
A2	2	1	1/2	3
A3	2	2	1	3
A4	1/3	1/3	1/3	1

Table 10.

Judgment matrix of searching initial target performance.

	B1	B2	B3	B4	B5	B6
B1	1	1	1/2	1/2	2	1/2
B2	1	1	1/2	1/3	2	1/2
B3	2	2	1	3	2	2
B4	2	2	1/3	1	2	2
B5	1/2	1/2	1/2	1/2	1	1/2
B6	2	2	1/2	1/2	2	1

Table 11.

Judgment matrix of parking procedure performance.

	B7	B8	B9	B10
B7	1	3	2	2
B8	1/3	1	2	1/2
B9	1/2	1/2	1	1/2
B10	1/2	2	2	1

Table 12.

Judgment matrix of parking effect.

	B11	B12	B13	B14
B11	1	1	1/2	1/2
B12	1	1	1/2	1/2
B13	2	2	1	3
B14	2	2	1/3	1

Table 13.

Judgment matrix of driver’s feelings during parking procedure.

	B15	B16	B17	B18
B15	1	1/2	3	1
B16	2	1	2	2
B17	1/3	1/2	1	1/2
B18	1	1/2	2	1

According to Table 14, the consistence rates of judgment matrixes are all lower than 0.1 and pass consistency test.

Table 14.

Each judgment matrix eigenvalues and maximum consistence rates’ calculation results.

	${\tilde{A}}_{1}$	${\tilde{A}}_{2}$	${\tilde{A}}_{3}$	${\tilde{A}}_{4}$	${\tilde{A}}_{5}$
$λ_{max}$	4.1213	6.3464	4.1425	4.1533	4.1171
CR	0.0454	0.0550	0.0534	0.0574	0.0439

Step 2.3. The determination and improvement of weight.

The weight of primary attributes for the overall performance of assisted parking system and the weight of secondary attributes for the overall performance of assisted parking system are shown in Figures 8 and 9, respectively.

Figure 8.

Primary attributes with respect to the assisted parking system performance overall weight.

Figure 9.

Secondary attributes with respect to the assisted parking system performance overall weight.

Step 3. The evaluation results and analysis of the overall performance of assisted parking system.

Step 3.1. Building two-tuple linguistics-based measure model.

Due to the limit of article length, there is only the list of tester’s assessment values for vehicle type A, as shown in Table 15.

Table 15.

Evaluation value of vehicle type A from test members.

Primary attributes	Secondary attributes	Expert evaluation values
Primary attributes	Secondary attributes	E1	E2	E3
A1	B1	(s₇, 0)	(s₇, 0)	(s₆, 0.2)
	B2	(s₆, 0)	(s₇, 0)	(s₅, 0.3)
	B3	(s₈, −0.39)	(s₈, −0.39)	(s₈, −0.39)
	B4	(s₆, 0.47)	(s₆, 0.47)	(s₆, 0.47)
	B5	(s₇, −0.24)	(s₇, −0.24)	(s₇, −0.24)
	B6	(s₈, −0.42)	(s₈, −0.42)	(s₈, −0.42)
A2	B7	(s₆, 0)	(s₇, 0)	(s₆, 0)
	B8	(s₆, 0)	(s₄, 0)	(s₅, 0)
	B9	(s₈, 0)	(s₈, 0)	(s₈, 0)
	B10	(s₈, 0)	(s₈, 0)	(s₈, 0)
A3	B11	(s₈, −0.49)	(s₈, −0.49)	(s₈, −0.49)
	B12	(s₈, −0.49)	(s₈, −0.49)	(s₈, −0.49)
	B13	(s₆, −0.12)	(s₆, −0.12)	(s₆, −0.12)
	B14	(s₅, 0)	(s₅, 0)	(s₅, 0)
A4	B15	(s₆, 0)	(s₅, 0)	(s₆, 0.4)
	B16	(s₇, 0)	(s₆, 0)	(s₇, −0.4)
	B17	(s₈, 0)	(s₇, 0)	(s₇, 0.1)
	B18	(s₆, 0)	(s₆, 0.4)	(s₅, 0.3)

Step 3.2. Calculate the measure value.

1. Calculate the measure value of the primary attributes provided by each tester. Calculate the corresponding measure value according to formula (4) with the calculation results shown in Table 16. Among these, $Δ^{- 1} (s_{k}, a_{k})$ is obtained by calculating according to formula (3) in Table 15. The weight $ω'_{i}$ is a result of the conversion of the values of weights in Figure 6 with the conversion results as shown in Table 17.

2. Calculate comprehensive measure value. Rank $Δ^{- 1} (s_{k 1}, a_{k 1})$ from Table 14 in descending order and get $B = (b_{1}, b_{2}, b_{3})^{T}$ . Then put $b_{i}$ and corresponding $v_{i}$ into formula (5), and get the comprehensive measure value of the overall performance of parking assistant system of type A car model. Similarly, the comprehensive measure value of car model B-H can be obtained. Draw the radar figure of the overall performance assessment of parking assistant system of different car models, as shown in Figure 10.

Table 16.

Measure values of primary attributes.

Primary attributes	Measure values
Primary attributes	E1	E2	E3
A1	6.9358	6.991537	6.844129
A2	7.134963	7.145102	6.99417
A3	5.700861	5.700861	5.700861
A4	6.576355	5.887601	6.29721

Table 17.

Weights of secondary attributes corresponding to primary attributes.

Primary attributes	Weights of secondary attributes corresponding to primary attributes
A1	ω ₁₁ = 0.065819603, ω₁₂ = 0.055737235, ω₁₃ = 0.225470493, ω₁₄ = 0.322765478, ω₁₅ = 0.202992647, ω₁₆ = 0.127214544
A2	ω ₂₁ = 0.29172523, ω₂₂ = 0.140793214, ω₂₃ = 0.231095624, ω₂₄ = 0.336385932
A3	ω ₃₁ = 0.100981006, ω₃₂ = 0.100981006, ω₃₃ = 0.220382542, ω₃₄ = 0.577655447
A4	ω ₄₁ = 0.289623456, ω₄₂ = 0.399761694, ω₄₃ = 0.088296715, ω₄₄ = 0.222318135

Figure 10.

Radar chart of assisted parking system overall performance evaluation.

3. Calculating the overall scores of different car models. Calculate the overall scores according to $(\tilde{s}, \tilde{a})_{score} = Δ (\sum_{i = 1}^{4} Δ^{- 1} (s_{ki}, a_{ki}) \times ω_{i}^{″})$ . Among these, the value of $Δ^{- 1} (s_{ki}, a_{ki})$ comes from Table 16, and the weight $ω_{i}^{″}$ comes from the comprehensive weight value in Figure 5. The calculated result is shown in Figure 11.

Figure 11.

Evaluation score histogram of each vehicle assisted parking system overall performance.

Results’ analysis

It can be seen from the weights in Figure 8, parking result (A3) is more important than the other three attributes with the weight of 0.514698; performance in parking procedure (A2) is the second most important attribute with the weight of 0.334763; performance of searching parking lot (A1) and drivers’ feelings in parking (A4) rank the last but one and the last with the weights of 0.127061 and 0.023478. Compared with performance of searching parking lot (A1), detection accuracy of parking longitudinal distance (B4), detection accuracy of parking lateral distance (B3), and maximum of velocity (B5) in secondary attributes are more important than other attributes, respectively, having the weight of 0.061127, 0.042701, and 0.038444. Compared with performance in parking procedure (A2), times of adjustment in garage (B10) is the most important having the weight of 0.118690. Compared with parking result (A3), the importance of angle between edge line of vehicle and lateral boundary of searching parking lot (B14) is obviously more important than the other three attributes having the weight of 0.221576, lateral offset relative to lateral boundary of searching parking lot (B13) is the second most important, and the importance of distance between obstacle ahead (B11) and distance between obstacle behind (B12) is similar. Compared with drivers’ feelings in parking (A4), probability of trust (B16) and involvement required level of driver (B15) are relatively important, respectively, with the weights of 0.029674 and 0.021499.

According to the total points of the overall performance evaluation of assisted parking system of different vehicle types in Figure 11, vehicle type F gets the highest points (7.74), namely, vehicle type F has the best overall performance of assisted parking system, and its subjective assessment belongs to the level slightly lower than “extremely good” according to the definition of two-tuple linguistics; vehicle types A, C, and E have the second highest points, followed by vehicle type D; vehicle types B, G, and H have approximate points much lower than vehicle type F. Vehicle type H has the lowest points, only 3.23 points, which has the worst overall performance of assisted parking system and whose subjective assessment belongs to the level slightly better than “bad.”

It is necessary to note that 4 points, namely, the common level in two-tuple linguistics, for mature assisted parking system is the critical value of the overall performance of assisted parking system. If lower than 4 points, it can be deemed that the assisted parking system has critical defects and needs to be redesigned or improved.

It can be seen from radar chart that vehicle types G and H have low points in parking result (A3), lower than 4 points, which means there are major design defects for the two vehicle types in parking result (A3) and redesign is needed to improve the performance in this aspect. Besides, vehicle types B, G, and H also have poor performance in parking procedure (A2), approximating 4 points and vehicle type B has good performance in the other aspects, so the focus can be put on the improvement of parking result (A3) and performance in parking procedure (A2) to improve the overall performance.

Vehicle type F’s assisted parking system has the best overall performance. But, compared with other three aspects, there is still space to improve in drivers’ feelings in parking (A4).

The total points of vehicle types A, C, and E all reach more than 6 points, namely, at a “better” level. For them, the performance attributes with relatively high weight coefficient and the attributes in an obviously inferior position can be first improved to improve the overall performance of assisted parking system.

Conclusion

Aiming at the problem that assisted parking system lacks complete and comprehensive performance evaluation method, and based on building comprehensive performance evaluation attribute system of assisted parking system, two-tuple linguistic analytic hierarchy process (2-TLAHP) is used to determine the weight of assessment attributes and two-tuple linguistic OWA operator is used to obtain the overall scores of assisted parking system of different vehicle types.

Aiming at the problem that the weight determined by hierarchy analysis method has not considered the randomness in parking experiment process, the traditional hierarchy analysis method determining weight is improved by raising an information entropy theory-based method.

The improvement direction of assisted parking system is raised through the analysis of the determined weight and parking evaluation experiment results to provide theoretical reference for the evaluation methods of the overall performance of assisted parking system.

Footnotes

Acknowledgements

The authors would also like to thank China Jiangsu University and USA California State University, Fresno.

Academic Editor: ZW Zhong

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was financially supported by The National Natural Science Fund (No. U1564201) and the CEEUSRO Innovative Capital Project in Science-Tech Bureau of Jiangsu Province (No. BY2012173). J.M. thanks Fresno for the support as a visiting scholar.

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	B1	B2	B3	B4	B5	B6
B1	1	1	1/2	1/2	2	1/2
B2	1	1	1/2	1/3	2	1/2
B3	2	2	1	3	2	2
B4	2	2	1/3	1	2	2
B5	1/2	1/2	1/2	1/2	1	1/2
B6	2	2	1/2	1/2	2	1

	B1	B2	B3	B4	B5	B6
B1	1	1	1/2	1/2	2	1/2
B2	1	1	1/2	1/3	2	1/2
B3	2	2	1	3	2	2
B4	2	2	1/3	1	2	2
B5	1/2	1/2	1/2	1/2	1	1/2
B6	2	2	1/2	1/2	2	1

	B1	B2	B3	B4	B5	B6
B1	1	1	1/2	1/2	2	1/2
B2	1	1	1/2	1/3	2	1/2
B3	2	2	1	3	2	2
B4	2	2	1/3	1	2	2
B5	1/2	1/2	1/2	1/2	1	1/2
B6	2	2	1/2	1/2	2	1