Optimizing assistive headphones for severe hearing impairment: A fuzzy AHP–PSO and COCOSO–game approach

Modern headphone models for severe hearing impairment

As can be seen in Table 2, this section will provide a concise summary of the most recent headphone models that are appropriate for individuals with severe hearing impairments.

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Table 2.

Brief review of modern headphone models for severe hearing impairment.

Model name	Country, year made	Mean features	References
Sennheiser RS 195 RF WirelessHeadphone System	Germany, 2015	– Designed for individuals with hearing impairments. –“Speech Mode” enhances vocal clarity. –“Music Mode” provides dynamic audio. – Wireless range: 100 m (328 ft, RF). – Battery life: ≈18 h (AAA NiMH rechargeable).	Sennheiser 42 Cadwell 43
AfterShokz Aeropex Bone Conduction Headphones	China, 2019	– Bone conduction technology. – Open-ear design for situational awareness. – Bluetooth 5.0 connectivity. – Battery life: 8 h. – Wireless range: 10 m (≈33 ft).	AfterShokz 44
Avantree HT280 Wireless Headphones	China, 2018	– 2.4 GHz RF technology (no audio delay). – Plug-and-play setup. – For TV and multimedia use. – Battery life: 12 h continuous use. – Wireless range: 30 m (≈100 ft).	Avantree 45
Nuraphone	Australia, 2017	– Hybrid over-ear + in-ear design. – Personalized hearing profile calibration. – Active Noise Cancelation (ANC). – Bluetooth 5.0 wireless. – Battery life: 20 h. – Wireless range: 10 m (≈33 ft).	Nurasound 46
Sony WH-1000XM4 Noise-Canceling Headphones	Japan, 2020	– Industry-leading noise cancelation. – Adaptive sound control and speak-to-chat. – Multipoint Bluetooth 5.0. – Battery life: 30 h (ANC on). – Wireless range: 10 m.	47
Bose SoundControl Hearing Aids	United States, 2021	– FDA-cleared self-fit hearing aids. – Bluetooth link via Bose Hear App. – Customizable profiles and speech focus. – Battery life: ≈18 h (per charge).	48
ClearSounds Quattro Pro Neckloop System	United States, 2016	– T-coil compatibility for hearing aid users. – Amplifies calls and conversations. – Omnidirectional microphone. – Battery life: ≈10 h. – Wireless range: ≈9 m (30 ft).	49
Phonak Roger On	Switzerland, 2021	– Directional speech-focus microphones. – Companion device for hearing aids. – Bluetooth and Roger wireless protocol. – Battery life: ≈8 h (typical use). – Wireless range: ≈10 m.	50
TV Ears Digital Wireless Headset System	United States, 2019	– Voice clarifying circuitry. – Lightweight under-chin design. – RF transmission for TV audio. – Battery life: ≈6 h per charge (NiMH). – Wireless range: ≈30 m (100 ft).	51
BeHear NOW Personal Amplifier	Israel, 2019	– Personal hearing amplifier with Bluetooth audio. – Adjustable profiles and noise reduction. – Neckband style. – Battery life: 12 h (hearing mode); 8 h streaming. – Wireless range: 10 m (typical Bluetooth).	52

The Sennheiser RS 195 RF Wireless Headphone System was launched in 2015 and produced in Germany. Intended for those with hearing problems, it includes a “Speech Mode” to improve vocal clarity by diminishing background noise and a “Music Mode” for providing a dynamic sound spectrum. It provides a wireless range of up to 328 ft, enabled by a charging transmitter port. The comfortable over-ear design with cushioned ear cups facilitates continuous use, and the 18-h battery life renders it suitable for lengthy listening sessions. The device is adaptable and compatible with televisions, audio systems, and digital devices.

The AfterShokz Aeropex Bone Conduction Headphones, introduced in 2019 in China, utilize bone conduction technology to convey sound through the cheekbones, circumventing the ear canal. Their open-ear design promotes situational awareness, while Bluetooth compatibility with a 30-foot range improves usage. These headphones are constructed with a lightweight titanium frame, ensuring both durability and comfort. Featuring an 8-h battery life and IP67 water resistance, they are ideal for busy consumers.

The Avantree HT280 Wireless Headphones, launched in 2018 and produced in China, are designed for television and media applications. They utilize 2.4 GHz RF technology to eliminate audio delay and provide a volume enhancement of up to 30% greater than conventional headphones. These headphones include a 100-foot wireless range and are easily configured with plug-and-play functionality. The over-ear, lightweight construction guarantees comfort, and the kit has a charging port.

The Nuraphone, introduced in 2017 and produced in Australia, integrates over-ear and in-ear configurations for enhanced noise isolation. It swiftly generates a customized hearing profile in less than a minute and includes active noise reduction as well as a “Social Mode” for perceiving ambient noises when necessary. The device provides a 20-h battery life and convenient on-ear controls, rendering it highly functional and user-friendly.

The Sony WH-1000XM4 Noise-Canceling Headphones, launched in 2020 in Japan, are acclaimed for their superior noise cancelation designed for loud surroundings. They incorporate intelligent auditory technology that modifies sound according to activity and location. These headphones have Bluetooth compatibility for hearing aids, offering a battery life of up to 30 h and rapid charging capabilities. Their lightweight, collapsible shape guarantees portability.

The Bose SoundControl Hearing Aids, launched in 2021 in the United States, are FDA-approved over-the-counter devices intended for moderate to severe hearing impairment. The Bose Hear app provides adjustable sound profiles, and the design is lightweight and practically imperceptible behind the ear. The device prioritizes speech clarity in noisy settings, offers a battery life of up to 18 h per charge, and does not necessitate professional fits.

The ClearSounds Quattro Pro Neckloop System, launched in 2016 in the United States, is intended for hearing aid wearers with T-coil functionality. It enhances audio for telephonic communication, music playback, and face-to-face discussions. The system has Bluetooth connectivity for hands-free operation and a removable omnidirectional microphone for improved voice clarity. The lightweight and ergonomic design guarantees extended comfort throughout wear.

The Phonak Roger On, introduced in 2021 in Switzerland, serves as an auxiliary device for hearing aids, particularly suited for group discussions or noisy settings. It employs directional microphones to concentrate on speech while minimizing ambient noise. The device features Bluetooth connectivity, is tiny, and is portable. It includes a rechargeable battery with enduring performance.

The TV Ears Digital Wireless Headset System, launched in 2019 in the United States, is engineered for delivering clear television audio without causing disturbance to others. The Voice Clarifying Circuitry enhances human speech frequencies. Featuring a wireless range of up to 50 ft, it enables adjustable volume separate from the television speakers. The lightweight under-the-chin headset configuration guarantees comfort throughout prolonged usage.

The BeHear NOW Personal Amplifier, launched in 2019 in Israel, enhances ambient sounds and Bluetooth audio for individuals utilizing hearing aids. It provides customizable sound profiles via the BeHear application. The lightweight in-ear configuration features noise reduction technology for improved clarity, rendering it suitable for music, calls, and direct discussions.

Assessment criteria for headphone models for severe hearing impairment

When evaluating assistive devices, particularly headphones designed for people with severe hearing impairments, it is necessary to define and prioritize assessment criteria. There are 20 criteria that are proposed by this research, and they are outlined in Table 3.

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Table 3.

The assessment criteria and their descriptions.

ID	Criteria	Annotations	Importance for evaluating headphones for severe hearing impairment
C1	Sound Amplification	Effectiveness in amplifying sounds for varying levels of hearing impairment.	Amplifying sound is crucial for users with hearing impairment to perceive audio more clearly and at their preferred level.
C2	Bone Conduction Technology	Ability to transmit audio via cheekbones, bypassing damaged ear structures.	Bone conduction allows sound to reach the inner ear without traditional pathways, aiding users who cannot hear via the eardrum.
C3	Hearing Aid Compatibility	Seamless integration with hearing aids or cochlear implants.	Integration with existing assistive devices ensures a cohesive auditory experience, making headphones more practical for hearing aid users.
C4	Dynamic Range Translation	Accuracy in representing varying sound intensities (e.g. soft vs. loud).	Accurate dynamic range is vital to prevent missing out on subtle audio cues, such as whispers or loud impacts, enhancing sound quality.
C5	Ambient Awareness	Allows situational awareness by mixing environmental sounds with audio output.	Maintaining awareness of surroundings is critical for safety, especially in outdoor or crowded environments.
C6	Ease of Setup	Intuitive setup and configuration, especially for non-technical users.	Easy setup ensures that even users without technical expertise can quickly enjoy the headphones.
C7	Comfort	Ergonomic and lightweight design for prolonged use.	Comfort is a key factor for long-term wear, ensuring that users can enjoy extended listening sessions without discomfort.
C8	Battery Life	Long-lasting battery with quick charging capabilities.	A long battery life is necessary to ensure the headphones last throughout the day, reducing the need for frequent recharging.
C9	Durability	Resistance to wear, sweat, water, and accidental drops.	Durability is crucial, particularly for active users, as headphones must withstand daily use and environmental conditions.
C10	Portability	Compact and foldable design for ease of transport.	Portability ensures that headphones are easy to carry for users who need them in different environments, such as commuting.
C11	Control Accessibility	Easy-to-operate buttons or touch controls for volume, modes, and playback.	Accessible controls make it easier for users to adjust settings without needing extra help, especially for those with dexterity challenges.
C12	Suitability for Activities	Adaptability for various uses like gaming, live events, or outdoor activities.	Versatility in different environments ensures that users can use their headphones in multiple contexts, improving their overall utility.
C13	Tactile Sensitivity Range	Ability to detect and differentiate low, mid, and high-frequency vibrations.	Tactile feedback allows users to “feel” different frequencies, which is essential for enhancing the sensory experience when hearing is limited.
C14	Speech Clarity	Enhancement of speech frequencies for improved verbal communication.	Clear speech enhancement is crucial for communication, especially for individuals who struggle with speech intelligibility due to hearing loss.
C15	Noise Cancelation	Ability to filter out background noise for focused listening.	Noise cancelation ensures a distraction-free environment, allowing users to focus on the desired audio without interference.
C16	Latency	Minimal delay in audio transmission, ensuring synchronization with visual media.	Low latency is essential for synchronization, especially when watching videos or participating in activities requiring real-time interaction.
C17	Feedback Modes	Haptic or visual feedback options for enhanced sensory engagement.	Haptic or visual feedback further engages the user’s other senses, making the experience richer, especially when auditory feedback is limited.
C18	AI Integration	Personalizes feedback and provides predictive adjustments.	AI integration can enhance the personalization of the experience, allowing the headphones to adjust based on the user’s preferences.
C19	Price-Performance Ratio	Cost-effectiveness relative to features and durability.	Evaluating the value of headphones ensures that users get a balanced mix of features and affordability, making it a practical investment.
C20	Environmental Awareness Mode	Highlights critical surrounding activities, such as alarms or footsteps.	Environmental awareness features add a layer of safety, allowing users to stay alert to important sounds in their surroundings.

Fuzzy AHP

The Fuzzy Analytic Hierarchy Process (Fuzzy AHP), an extension of Saaty’s ⁵³ Analytic Hierarchy Process (AHP) utilizes fuzzy set theory to mitigate uncertainties and ambiguities in decision-making. Fuzzy AHP improves the robustness of evaluations in complicated circumstances by enabling decision-makers to articulate preferences and uncertainties using fuzzy numbers. ⁵⁴ This approach has been extensively utilized across multiple domains, including technology assessment, owing to its proficiency in managing ambiguous data and subjective evaluations successfully. ⁵⁵ This study uses Fuzzy AHP to prioritize criteria for selecting ideal headphone models, thereby establishing a more trustworthy decision-making framework.

Define the decision-making problem by determining all the criteria, sub-criteria, and the alternatives.

Create pairwise comparison matrices using triangular fuzzy numbers (TFNs) for each criterion and alternative.

The fuzzy pairwise comparison matrix A ~ for n criteria:

A ~ = [ a ~ ij ] , where a ~ ij = ( l ij , m ij , u ij )

(1)

l _ij is lower bound, m _ij is most likely value, and u _ij is upper bound.

Calculate the fuzzy geometric mean of each criterion i of the normalized matrix A ~ N :

r ~ i = ( Π j = 1 n l ij ) 1 n , ( Π j = 1 n m ij ) 1 n , ( Π j = 1 n u ij ) 1 n

(2)

Normalize the fuzzy geometric means to obtain fuzzy weights:

w ~ ij = ( l i ∑ i = 1 n u i , m i ∑ i = 1 n m i , u i ∑ i = 1 n l i )

(3)

Calculate the Consistency Index (CI) and Consistency Ratio (CR) using the following equations:

Consistency Index : CI = λ max − n n ,

λ _max is the largest eigenvalue of the matrix A ~ and n is the number of criteria.

Consistency Ratio : CR = CI RI

where RI is the Random Consistency Index based on matrix size n. When CR < 0 . 1 , the matrix is consistent.

Combine the experts’ weights using the Fuzzy Weighted Geometric (FWG) operator:

w ~ i = ( Π k = 1 m l ik w k , Π k = 1 m m ik w k , Π k = 1 m u ik w k )

(4)

where w _k is the weight of the k decision-maker, and m is the number of experts.

Using any method of defuzzification on the w ~ i to get on crisp values for ranking ⁵⁶ :

D ( w ~ i ) = ( u i + 4 m i + l i ) 6

(5)

Rank the criteria based on the crisp value of D ( w ~ i ) . Higher values indicate greater importance or preference.

Multiply the weights of criteria w _i by the relative performance of each alternative p _ik .

Compute the overall scores for each alternative:

S k = ∑ i = 1 n w i · p ik

(6)

w _i : Weight of criterion i, p _ik : Performance of alternative k on criterion i.

Rank the alternatives based on their scores S _k . Higher scores indicate better alternatives.

Although Fuzzy AHP provides a solid basis for deriving expert-driven weights, the results can still carry some degree of subjectivity and inconsistency. To strengthen the reliability of these weights, we refined them using Particle Swarm Optimization (PSO). Unlike methods that rely on gradients, PSO operates through a population-based search over a constrained solution space, which makes it particularly suitable for multi-criteria decision-making. Compared with other metaheuristic approaches, such as Genetic Algorithms (GA) or Differential Evolution (DE), PSO is more straightforward to implement, requires fewer control parameters, and generally has a lower computational cost. ⁵⁷ These advantages make it a practical choice for refining subjective weights in a way that is both reproducible and efficient. Previous studies have also shown that PSO and its hybrid variants can enhance the consistency of AHP weights and reduce decision-making uncertainty.^35,38 In our study, the PSO fitness function was structured to achieve three goals: (i) to maintain compatibility with the Fuzzy AHP pairwise comparisons, (ii) to align with performance-related signals, and (iii) to preserve feasibility of the weight distribution. This design ensures that the optimization process remains conservative-respecting the original expert input while making modest, data-driven adjustments. Additionally, we monitored the Consistency Index and Consistency Ratio (CI/ /CR) during the refinement process to confirm that the adjusted weights remained within acceptable limits.

Particle swarm optimization PSO

PSO is a metaheuristic method introduced in 1995 and has since been applied to a wide range of applications. In this context, we will use PSO to optimize the weights determined by the Fuzzy AHP (Fuzzy Analytic Hierarchy Process) method. The input will include factors such as the expert scores for each criterion. The key steps of PSO are as follows:

Start with fuzzy AHP-derived weights w ~ for criteria C 1 , C 2 , … , C n

Ensure weights are normalized: ∑ i = 1 n w i = 1 , and w i ≥ 0 .

Each particle represents a weight vector W = [ w 1 , w 2 , … , w n ] .

Initialize particles around w ~ with small random perturbations to ensure exploration.

Use the Consistency Index (CI) from AHP to ensure optimized weights align with expert judgments.

Let RI be the random index for the matrix size n.

Define the Consistency Ratio: CR = CI RI , where Consistency Index: CI = λ max − n n , and λ _max is the largest eigenvalue of the matrix A ~ and n is the number of criteria. Our goal is to minimize CR.

We will include a term that minimizes the error between weights and normalized performance scores

S = [ s 1 , s 2 , … , s n ] E = ∑ i = 1 n | w i − s i ∑ j = 1 n s j | 2

(7)

Enforce w i ≥ 0 , and ∑ i = 1 n w i using penalty terms:

P norm = | 1 − ∑ i = 1 n w i | , P neg = ∑ i = 1 n max ( 0 , w i )

(8)

Combine the components with appropriate weights ( α , β , γ , δ )

F ( W ) = α · CR + β · E + γ P norm + δ P neg

(9)

In this study, we aim to balance four key aspects: (i) preserving the Fuzzy AHP pairwise-comparison structure through the AHP consistency term; (ii) aligning the weights with experts’ criterion-level importance scores; and (iii and iv) softly enforcing normalization and non-negativity. The fitness function applies weighting coefficients ( α , β , γ , δ ) set as α = 0 . 5 , β = 0 . 3 , γ = 0 . 1 , δ = 0 . 1 . A larger α anchors PSO as a refinement of Fuzzy AHP rather than a replacement, consistent with PSO–AHP hybrids that preserve the hierarchical structure while enabling data-driven adjustment.^35–38 The alignment term is given secondary influence ( β = 0 . 3 ) to ensure that expert scores guide, but do not dominate, the pairwise judgments. Penalty terms are kept small ( γ = 0 . 1 , δ = 0 . 1 ) because feasibility is enforced through projection after each PSO update; these terms act as regularizes to control boundary behavior without steering the solution away from its core objective. A sensitivity analysis over ( α , β , γ , δ ) is provided in Appendix 1, demonstrating that the chosen setting yields the closest agreement with the FAHP baseline while stabilizing downstream decisions.

Our objective is to minimize F(W), a fitness function designed to optimize decision-making weights. This function is flexible, balancing subjective and objective criteria, while also incorporating a consistency check to ensure that weight remains aligned with expert pairwise judgments. Furthermore, it supports data integration by including objective performance metrics when available, thus providing a more comprehensive and robust optimization framework.

Step 4: PSO Implementation

Velocity update:

v ( t + 1 ) = ω · v ( t ) + c 1 r 1 ( P b e s t − W ( t ) ) + c 2 r 2 ( g b e s t − W ( t ) )

(10)

Position update:

W ( t + 1 ) = W ( t ) + v ( t + 1 )

(11)

where ω is the inertia wight, c 1 , c 2 are acceleration coefficients, and r 1 , r 2 are random numbers in [0, 1].

Once the stopping criteria are met, the final weight vector W is considered optimal, having minimized the fitness function while adhering to the constraints and balancing both subjective and objective criteria.

In this study, PSO was implemented using a swarm of 30 particles and a maximum of 200 iterations. Particle positions were initialized uniformly in the interval [0, 1] and projected onto the probability simplex to satisfy the weight-sum constraint. Velocities were initialized within ±0.2. The inertia weight decreased linearly from 0.9 to 0.4, and the cognitive and social coefficients were both set to 1.5. After each update, particle positions were clipped to [0, 1] and re-projected to the simplex to maintain feasibility. Convergence was achieved when the change in the best global fitness value dropped below 10⁻⁶ for 25 consecutive iterations or when the iteration limit was reached. A fixed random seed (42) was used to ensure full reproducibility.

Fuzzy combined compromise solution (Fuzzy COCOSO) method

The Fuzzy COCOSO method is an advanced MCDM technique that integrates fuzzy logic to handle uncertainty and imprecision in decision data. Building upon the foundational steps of the COCOSO method, the fuzzy extension incorporates fuzzy numbers to better represent ambiguous information. Below is a detailed breakdown of the Fuzzy COCOSO method, including mathematical equations and references to the specified studies.

Define the decision-making problem by determining all the for n criteria and m alternatives.

Create fuzzy matrix using triangular fuzzy numbers (TFNs) for each criterion and alternative.

The fuzzy pairwise comparison matrix X ~ for n criteria:

X ~ = [ x ~ ij ] , where x ~ ij = ( l ij , m ij , u ij ) , i = 1 , 2 , … , m ; j = 1 , 2 , … , n

(12)

l _ij is lower bound, m _ij is middle value, u _ij is upper bound.

Normalize the fuzzy geometric means to obtain fuzzy weights:

r ~ ij = { ( l ij u j max , m ij m j max , u ij l j max ) for benfit criteria ( l j max u ij , m j max m ij , u j max l ij ) for cost criteria

(13)

As the steps in the above section

Step 5: Compute the Weighted Normalized Decision Matrix

v ~ ij = r ~ ij ⊗ w j

(14)

⊗ denotes the multiplication of a fuzzy number by a scalar weight.

Compute the aggregated scores for each alternative using both the sum and product of weighted normalized values:

Sum of the weighted normalized values:

S i = ∑ j = 1 n v ~ ij

(15)

Product of the weighted normalized values:

P i = Π j = 1 n ( v ~ ij ) w j

(16)

Convert the fuzzy aggregated scores S ~ i and P ~ i into crisp values using the centroid method:

Defuzzified Value = ( u i + 4 m i + l i ) 6

(17)

Step 8: Calculate the Combined Compromise Score.

Integrate the defuzzified scores to obtain a combined compromise score for each alternative:

C i = α × S i + ( 1 − α ) × P i

(18)

where α is a compromise coefficient determined by the decision-maker.

Rank the alternatives based on the combined compromise scores C _i , Alternatives with higher C _i , values are considered more favorable.

Fuzzy Zero-Sum Game analysis

The Fuzzy Zero-Sum Game Analysis introduces fuzzy intervals to account for uncertainties in payoffs within a traditional Zero-Sum-Game framework. The payoffs are expressed as triangular fuzzy numbers ( l , m , u ) , representing lower, middle, and upper bounds, respectively.

Incorporate the weights of the criteria W = ( w 1 , w 2 , … , w k ) where k is the number of criteria.

For each entry in the fuzzy payoff matrix by representing each element of the utility matrix as a triangular fuzzy number ( l ij , m ij , u ij ) :

l _ij The lower bound represents the minimum possible payoff.

m _ij : The middle value, representing the most likely payoff.

u _ij The upper bound represents the maximum possible payoff.

l ij W = ∑ k = 1 K w k · l ij k , m ij W = ∑ k = 1 K w k · m ij k , u ij W = ∑ k = 1 K w k · u ij k

(19)

Construct the weighted fuzzy payoff matrix using l W , m W , and u W .

Normalize each element of the fuzzy payoff matrix to ensure comparability between payoffs. Normalization can be performed using the following equations:

l ′ ij = l ij − min ( l ) max ( u ) − min ( l ) , m ′ ij = m ij − min ( l ) max ( u ) − min ( l ) , u ′ ij = u ij − min ( l ) max ( u ) − min ( l )

(20)

Where max ( u ) & min ( l ) are the global minimum and maximum values across all payoffs. This ensures consistency across strategies.

Player 1 (Maximizer):

Maximize z

∑ i = 1 m p i · l ij ≥ z , ∀ j ( for lower bounds constraint ) ∑ i = 1 m p i · u ij ≥ z , ∀ j ( for upper bounds constraint ) ∑ i = 1 m p i = 1 , p i ≥ 0 , ∀ i

(21)

Player 2 (Minimizer):

Maximize w ∑ j = 1 n q j · l ij ≤ w , ∀ i ( for lower bounds constraint ) ∑ j = 1 n q j · u ij ≤ w , ∀ i ( for upper bounds constraint ) ∑ j = 1 n q j = 1 , q j ≥ 0 , ∀ j

(22)

Python software is used to solve the LP problems for both players:

Step 5: Interpret the Results

Analyze the results to understand the optimal strategies and outcomes for both players:

Fuzzy AHP for determining the criteria weights

In this part, criteria weights are calculated based on the insights of four experts specializing in technology pertinent to headphone models for profound hearing impairment. Each expert’s perspective was accorded equal importance to guarantee a balanced assessment of the criteria and strategic aims. The decision-making team comprised an assistive technology specialist, a biomedical engineer, a rehabilitation expert, and a market analyst. They provided substantial insights to the evaluation process by combining their knowledge in usability, technological innovation, practical application, and market dynamics. As mentioned in the methodology, the criteria weights were derived from expert pairwise comparisons and refined using PSO. This comprehensive review examined both the technical and practical dimensions of headphone performance and adoption, providing a balanced analysis.

The Fuzzy AHP steps outlined in subsection (3-a) were utilized to determine the criteria weights. The final weights allocated to the criteria are presented in Table 4.

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Table 4.

Final weight of criteria using fuzzy AHP.

ID	Criteria	Weight	Rank	ID	Criteria	Weight	Rank
C1	Sound Amplification	0.0628	2	C11	Control Accessibility	0.053382	6
C2	Bone Conduction Technology	0.053382	6	C12	Suitability for Activities	0.048258	10
C3	Hearing Aid Compatibility	0.058495	3	C13	Tactile Sensitivity Range	0.043119	14
C4	Dynamic Range Translation	0.048258	10	C14	Speech Clarity	0.0636	1
C5	Ambient Awareness	0.043119	14	C15	Noise Cancelation	0.058495	3
C6	Ease of Setup	0.048258	10	C16	Latency	0.043119	14
C7	Comfort	0.058495	3	C17	Feedback Modes	0.037958	19
C8	Battery Life	0.053382	6	C18	AI Integration	0.043119	14
C9	Durability	0.048258	10	C19	Price-Performance Ratio	0.053382	6
C10	Portability	0.043119	14	C20	Environmental Awareness Mode	0.037958	19

The findings provide light on the weight of each criterion, which is helpful for making decisions. With a weight of 0.0636, Speech Clarity (C14) takes first place as the most essential criterion. This highlights the importance of audible and comprehensible audio, especially for applications involving speech and communication. Second in importance with a weight of 0.0628, Sound Amplification (C1) highlights the significance of volume and clarity, particularly for users with hearing problems. Third place goes to Noise Cancelation (C15), whose 0.0585 weight reflects its function in improving the listening experience by reducing interference from outside noise. Criteria of moderate importance encompass Hearing Aid Compatibility (C3) and Comfort (C7), both ranked third with a weight of 0.0585. These criteria are vital for guaranteeing accessibility for users with hearing aids and assuring comfort during prolonged use. Bone Conduction Technology (C2), Battery Life (C8), and Price-Performance Ratio (C19) are ranked sixth, each assigned a weight of 0.0534, signifying its moderate significance. Bone conduction is essential for particular user demographics, battery longevity is a pragmatic concern, and the price-performance ratio is a significant determinant for budget-conscious consumers. Conversely, Feedback Modes (C17) and Environmental Awareness Mode (C20) are the least significant criteria, both positioned 19th with a weight of 0.0380. These features are specialized and not commonly emphasized by the majority of consumers. Likewise, Tactile Sensitivity Range (C13), Latency (C16), and AI Integration (C18) are ranked 14th with a weight of 0.0431, signifying that they are not predominant concerns for most users.

In summary, Speech Clarity, Sound Amplification, and Noise Cancelation are the crucial factors for assessing headphones, as they directly influence fundamental functionality and user experience. Conversely, Feedback Modes and Environmental Awareness Mode are the least significant, embodying specialized attributes that may not pertain to all users. These insights can inform headphone design, marketing, and selection, ensuring that the most desired attributes are highlighted while less vital characteristics are tailored for certain user demographics. The aggregated FAHP matrix satisfied the AHP consistency requirement (CI = 0.05996, RI = 1.6301, CR = 0.0368), confirming that the expert judgments were coherent and internally consistent.

Particle Swarm Optimization (PSO) for optimizing the criteria weights

The PSO procedure was applied to refine the FAHP-derived weight vector in a 20-dimensional simplex-constrained search space. The swarm consisted of 30 particles with a maximum of 200 iterations, following the parameter settings described in Section 3.2. The inertia weight decreased from 0.9 to 0.4, the velocity was limited to ±0.2, and both cognitive and social coefficients were set to 1.5. This combination provided stable convergence during tuning experiments and avoided premature stagnation. The fitness function incorporated consistency and alignment terms to ensure compatibility between expert judgments and the optimized weights. All PSO runs used the same fixed random seed (42) for reproducibility.

Table 5 displays the mean scores attributed by four experts to each criterion for headphone evaluation. The scores represent the consensus of experts regarding the significance of each attribute. Criteria C1 (Sound Amplification) and C14 (Speech Clarity) attained the maximum score of 10, signifying their status as the most essential elements. C3 (Hearing Aid Compatibility), C7 (Comfort), and C15 (Noise Cancelation) received excellent scores of 9, underscoring their importance in headphone performance and user experience. Criteria of moderate importance, including C2 (Bone Conduction Technology), C8 (Battery Life), C11 (Control Accessibility), and C19 (Price-Performance Ratio), received a score of 8, indicating their practical significance. C5 (Ambient Awareness), C10 (Portability), C13 (Tactile Sensitivity Range), C16 (Latency), C17 (Feedback Modes), C18 (AI Integration), and C20 (Environmental Awareness Mode) received lower scores, ranging from 5 to 7, indicating that experts consider these aspects to be of lesser priority. The scores correspond with the Fuzzy AHP weights, underscoring the experts’ agreement on the primacy of sound quality, comfort, and utility over specialized or secondary features.

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Table 5.

The experts’ average scores.

ID	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20
Score	10	8	9	7	6	7	9	8	7	6	8	7	6	10	9	6	5	6	8	5

In order to bring the Fuzzy AHP weights into line with the experts’ ratings, the PSO approach was used to refine them. To find the optimal weights, the PSO algorithm minimized a fitness function that took into account the following factors: conformity with objective performance ratings, consistency with Fuzzy AHP evaluations, and non-negativity and normalization constraints. A more balanced and data-driven prioritization of criteria is reflected in the final weights, as indicated in Table 6. While hearing aid compatibility (C3, 0.0622) and sound amplification (C1, 0.0619) are still important criteria, speech clarity (C14, 0.0626) is still at the top. The relevance of Noise Cancelation (C15, 0.0547) and the Price-Performance Ratio (C19, 0.0594) in performance and cost concerns is demonstrated by their high rankings. Because of the specific uses for which they were developed, lower-ranking criteria like Feedback Modes (C17, 0.0350) and Environmental Awareness Mode (C20, 0.0357) continue to receive less weight.

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Table 6.

Final weight of sub-criteria using PSO.

ID	Criteria	Weight	Rank	ID	Criteria	Weight	Rank
C1	Sound Amplification	0.061937	3	C11	Control Accessibility	0.051824	10
C2	Bone Conduction Technology	0.052081	8	C12	Suitability for Activities	0.047376	13
C3	Hearing Aid Compatibility	0.062243	2	C13	Tactile Sensitivity Range	0.042499	17
C4	Dynamic Range Translation	0.047092	14	C14	Speech Clarity	0.0626	1
C5	Ambient Awareness	0.040487	18	C15	Noise Cancelation	0.054757	5
C6	Ease of Setup	0.048249	12	C16	Latency	0.044719	16
C7	Comfort	0.053075	7	C17	Feedback Modes	0.035046	20
C8	Battery Life	0.052046	9	C18	AI Integration	0.046691	15
C9	Durability	0.05325	6	C19	Price-Performance Ratio	0.059461	4
C10	Portability	0.048873	11	C20	Environmental Awareness Mode	0.035694	19

Figure 2, Tables 4, and 6 indicate that the PSO-optimized weights differ slightly from the Fuzzy AHP results, indicating a data-driven approach. For example, C14 for Speech Clarity and C1 for Sound Amplification were given slightly different weights to make them more in line with the experts’ ratings, but they were still at the top. In the optimized model, Hearing Aid Compatibility (C3) took center stage, highlighting its significance. As a result of its real-world relevance, Price-Performance Ratio (C19) also rose to popularity. Feedback Modes (C17) and Environmental Awareness Mode (C20), two less essential criterion, remained in their low rankings despite seeing no modifications. All things considered, the PSO findings offer a more accurate and impartial weighting system that maintains the fundamental priorities established by Fuzzy AHP.

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Figure 2.

Comparison of the criteria weights using Fuzzy AHP and PSO.

With the use of expert scores and the consistency of paired assessments, the Fuzzy AHP weights were effectively optimized using PSO. According to the findings, the three most important factors for judging headphones are speech clarity (C14), compatibility with hearing aids (C3), and sound amplification (C1). Noise Cancelation (C15) and the Price-Performance Ratio (C19) were also prioritized during optimization to meet consumer expectations for performance and price. Confirmation of lower-ranked criteria’ perceived lack of importance lends credence to their specialized uses, such as Feedback Modes (C17) and Environmental Awareness Mode (C20). In order to prioritize the most valued features while keeping them aligned with expert judgments and objective performance measurements, these findings offer a comprehensive and data-driven paradigm for decision-making in headphone design and evaluation.

Figure 2 compares the weights derived from Fuzzy AHP and the PSO-refined configuration. The figure highlights how PSO adjusts a subset of high-influence criteria, particularly Speech Clarity (C14), Hearing Aid Compatibility (C3), and Sound Amplification (C1), while preserving the overall structure of the expert-based FAHP weights.

Headphone models evaluation

In this part, we give the ranking results of the headphone models utilizing the Fuzzy COCOSO and Zero-Sum-Game methodologies. Figure 3 and Table 7 present the findings and comparative efficacy of the examined headphones. These strategies were utilized to rank the alternatives based on the weighted criteria established in the previous section.

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Figure 3.

Headphone models ranking using Fuzzy COCOSO and Fuzzy Zero-Sum Game methods.

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Table 7.

Comparison of headphone models ranking using Fuzzy COCOSO and Fuzzy Zero-Sum Game methods.

Headphone Model	Fuzzy COCOSO				Fuzzy Zero-Sum Game method
	Sum	Product	Scores	Ranking	Scores	Ranking
Sennheiser RS 195 RF Wireless Headphone System	0.3909	1.62E–33	0.19544755	7	0.245621	6
AfterShokz Aeropex Bone Conduction Headphones	0.5078	1.00E–30	0.25389995	4	0.27882	4
Avantree HT280 Wireless Headphones	0.330775	2.25E–34	0.16538769	8	0.209278	8
Nuraphone	0.327219	6.75E–34	0.16360932	10	0.219925	7
Sony WH-1000XM4 Noise-Canceling Headphones	0.477643	6.97E–31	0.23882137	5	0.204329	10
Bose SoundControl Hearing Aids	0.577306	1.55E–29	0.28865306	1	0.302813	1
ClearSounds Quattro Pro Neckloop System	0.475546	6.34E–31	0.23777323	6	0.26647	5
Phonak Roger On	0.577306	1.55E–29	0.28865306	1	0.302813	1
TV Ears Digital Wireless Headset System	0.330775	2.25E–34	0.16538769	8	0.209278	8
BeHear NOW Personal Amplifier	0.577306	1.55E–29	0.28865306	1	0.302813	1

Figure 3 and Table 6 summarize the ranking outcomes from both Fuzzy COCOSO and the Fuzzy Zero-Sum Game. The figure visually demonstrates the strong agreement between the two methods, particularly for the highest-ranked alternatives such as Bose SoundControl Hearing Aids and Phonak Roger On. It also highlights the relative underperformance of models such as Avantree HT280 and TV Ears, reinforcing the consistency between additive-multiplicative scoring and strategic payoff analysis

In detail, the Bose SoundControl Hearing Aids, Phonak Roger On, and BeHear NOW Personal Amplifier are the top-performing models for both methods. These achieving the highest scores (0.2887 in FUZZY COCOSO and 0.3028 in Fuzzy Zero-Sum Game). This is due to the strong performance of these models in important criteria such as speech clarity, hearing aid compatibility, and noise cancelation. The Avantree HT280 Wireless Headphones and TV Ears Digital Wireless Headset System received a lower ranking and poor scores in both methods due to its poor performance in the important criteria.

While the top and bottom rankings are very similar across the board, there are some little differences. For example, the Sony WH-1000XM4 Noise-Canceling Headphones rank fifth in FUZZY COCOSO but fall to 10th in the Fuzzy Zero-Sum Game. This is probably because the two systems take different approaches to calculating and weighting competition scores. The AfterShokz Aeropex Bone Conduction Headphones consistently perform well, as they rank fourth in both FUZZY COCOSO and the Fuzzy Zero-Sum Game. These differences illustrate how the two approaches work well together; although the Fuzzy Zero-Sum Game prioritizes competitive performance, FUZZY COCOSO focuses on weighted aggregation.

The test results indicate that the top-performing headphone models in terms of essential characteristics such as noise cancelation, hearing aid compatibility, and voice clarity are the Phonak Roger On, the BeHear NOW Personal Amplifier, and the Bose SoundControl Hearing Aids. The dependability and utility of both strategies for users with particular needs, such as hearing assistance, are underscored by the uniformity in rankings overall. The TV Ears Digital Wireless Headset System and Avantree HT280 Wireless Headphones, both of inferior ranking, may require enhancements to enhance their competitiveness. The minor differences in outcomes between FUZZY COCOSO and Fuzzy Zero-Sum Game might be attributed to the distinct procedures employed by the two approaches: The Fuzzy Zero-Sum Game prioritizes relative performance and competitive scoring, in contrast to FUZZY COCOSO’s weighted aggregation of criteria. These disparities underline the importance of employing multiple evaluation approaches to provide a thorough understanding of model performance. The comprehensive findings provide valuable insights for both buyers and sellers, guiding planning and development toward elements most pertinent to actual purchases.

The dual use of Fuzzy COCOSO and Fuzzy Zero-Sum Game provides complementary insights. While Fuzzy COCOSO emphasizes compromise-based aggregation across weighted criteria, the Fuzzy Zero-Sum Game highlights competitive interactions and equilibrium strategies. The convergence of results across these two perspectives increases the robustness of the rankings and enhances confidence in the reliability of the findings.

SWOT analysis

By applying the SWOT analysis to a wide variety of headphones made for the deaf and hard of hearing, this study examines the strategic elements that have an impact on these products. Using a SWOT (Strengths, Weaknesses, Opportunities, and Threats) analysis, this study will try to find major competitive advantages, improvement spots, market potential, and outside obstacles. For a thorough comprehension of the strategic environment, the SWOT matrix classifies elements including cutting-edge audio technology, accessibility for those with hearing loss, battery life, price, and current market trends. With this methodical strategy, you may find growth and innovation opportunities in a competitive and ever-changing business, and make better judgments overall. Table 8 summarizes the strategies together with their descriptions.

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Table 8.

SWOT analysis matrix for headphone models: strategic factors and classification.

SWOT factor	Headphone models	Strategy code	Strategic factors
Strengths	Sennheiser RS 195, Nuraphone, Sony WH-1000XM4	S1	Advanced sound quality with customizable profiles, dynamic sound modes (e.g. Speech Mode, Music Mode).
	AfterShokz Aeropex, BeHear NOW, Bose SoundControl	S2	Specialized features for hearing-impaired users: bone conduction, sound amplification, speech clarity modes.
	Avantree HT280, TV Ears Digital	S3	Long wireless range and low-latency for clear TV/media listening without delay (100–150 ft, respectively).
	Sennheiser RS 195, Avantree HT280	S4	Excellent battery life (18–30 h) ensuring extended use without frequent recharging.
Weaknesses	AfterShokz Aeropex, TV Ears Digital	W1	Shorter battery life (8–12 h) compared to models with longer durations.
	Nuraphone, Bose SoundControl	W2	High cost, which may limit accessibility for price-sensitive users, especially in comparison to basic hearing aids.
	Sennheiser RS 195, Avantree HT280	W3	Limited versatility—mainly designed for TV/media use or as hearing aids, reducing broader application.
	AfterShokz Aeropex, BeHear NOW	W4	Sound quality may not be adequate for users with profound hearing loss or those seeking richer audio.
Opportunities	Nuraphone, Sony WH-1000XM4, BeHear NOW	O1	Rising demand for personalized, customizable hearing solutions tailored to individual hearing needs.
	Sennheiser RS 195, Avantree HT280	O2	Growing senior population and market expansion for assistive devices targeted at hearing-impaired individuals.
	AfterShokz Aeropex, Phonak Roger On	O3	Opportunities to integrate with hearing aids and other assistive technologies for an improved user experience.
	Bose SoundControl, ClearSounds Quattro Pro	O4	Expanding into over-the-counter hearing aid markets, meeting the demand for more accessible and affordable solutions.
Threats	Nuraphone, Sony WH-1000XM4, Sennheiser RS 195	T1	Intense competition from traditional hearing aids and advanced specialized assistive listening devices.
	AfterShokz Aeropex, BeHear NOW	T2	Resistance to adopting new technologies from users accustomed to traditional hearing aids or simpler devices.
	Avantree HT280, TV Ears Digital	T3	Competing products offering similar features at lower prices, reducing the market share for these models.
	Bose SoundControl, ClearSounds Quattro Pro	T4	Regulatory barriers for over-the-counter hearing aids and market restrictions limiting broader adoption.
	Sennheiser RS 195, AfterShokz Aeropex	T5	Price sensitivity among the target audience, limiting accessibility to higher-end assistive listening devices.

The SWOT analysis table provides a thorough and comprehensive assessment of the strategic elements affecting different headphone models, especially those intended for hearing-impaired individuals and general consumers. It delineates strengths, including superior sound quality, dynamic sound modes, bone conduction, and configurable profiles, which directly cater to the requirements of hearing-impaired individuals. Weaknesses are distinctly classified, emphasizing particular concerns such as battery life restrictions and product applicability constraints (e.g. TV/media-centric vs multifunctional). Opportunities highlight emerging industry trends, including the aging demographic, the need for customized solutions, and the incorporation of other assistive technology. Simultaneously, threats pertain to competition from conventional hearing aids and economical alternatives, including price sensitivity within the target audience. This matrix offers a definitive and pragmatic framework for strategic decision-making, facilitating a comprehensive grasp of competitive positioning, areas for enhancement, and prospective growth prospects in a dynamic market.

To systematically analyze the SWOT matrix, we applied the fuzzy COCOSO method. This approach ranks strategic factors by combining the sum and product of weighted scores, providing a balanced and reliable evaluation. Using this method, we were able to prioritize the strengths, weaknesses, opportunities, and threats (SWOT) based on their relative importance and impact. As a result, the analysis becomes more objective and dependable, supporting better-informed strategic decisions.

The fuzzy COCOSO method offers several key benefits for SWOT analysis. First, it combines compromise and aggregation strategies, leading to a more balanced prioritization of factors. Second, the fuzzy setting makes it possible to capture expert opinions more flexibly, reducing the uncertainty and vagueness often present in strategic evaluations. Third, compared with classical SWOT or other ranking methods, fuzzy COCOSO produces more stable and consistent results across different scenarios, which strengthens the reliability of the recommendations.

This approach integrates both compromise and aggregation strategies, enabling a more balanced prioritization of SWOT factors. Second, the fuzzy environment allows expert opinions to be expressed with flexibility, addressing uncertainty and vagueness in strategic assessments. Third, compared to classical SWOT or other ranking methods, Fuzzy COCOSO produces stable and consistent rankings across scenarios, enhancing the robustness of strategic recommendations. These features make Fuzzy COCOSO particularly suitable for SWOT-based strategy development in assistive technology contexts.

The strengths evaluation findings, presented in Table 9, indicate that S2 (Specialized features for hearing-impaired users: bone conduction, sound amplification, voice clarity modes) occupies the top position with a score of 0.351634. This underscores the essential necessity of catering to the distinct requirements of hearing-impaired individuals via innovative technologies. S1 (Superior sound quality with configurable profiles and dynamic sound modes) ranks second, highlighting the importance of premium audio and personalization. S3 (extended wireless range and low latency for television/media listening) and S4 (superior battery longevity) occupy the third and fourth positions, respectively, signifying that although these attributes are advantageous, they are somewhat less significant than the foremost two strengths. These rankings highlight the importance of emphasizing user-centric features and sophisticated technology capabilities in the development of products.

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Table 9.

Strengths evaluation and ranking.

	Sum	Product	Scores	Ranking
S1	0.556007	6.04E–31	0.278003	2
S2	0.703268	7.45E–29	0.351634	1
S3	0.374281	1.14E–33	0.18714	3
S4	0.204078	1.15E–37	0.102039	4

The assessment of weaknesses, detailed in Table 10, designates W4 (Sound quality may not be sufficient for users with substantial hearing loss or those desiring enhanced audio) as the most significant problem, achieving a top rank with a score of 0.315025. This indicates that enhancing audio quality for individuals with profound hearing impairment should be a primary area of emphasis. W1 (Reduced battery longevity) is positioned second, underscoring the necessity for improved battery efficiency in specific models. W3 (limited versatility—primarily intended for television/media applications or as hearing aids) and W2 (high cost) occupy the third and fourth positions, respectively, signifying that although these factors are important, they are less critical than sound quality and battery longevity. These findings underscore the necessity of overcoming technical constraints and financial obstacles to enhance customer happiness and market competitiveness.

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Table 10.

Weaknesses evaluation and ranking.

	Sum	Product	Scores	Ranking
W1	0.49942	1.033E–30	0.24971	2
W2	0.327321	1.37E–33	0.16366	4
W3	0.365264	1.11E–32	0.182632	3
W4	0.630051	5.28E–29	0.315025	1

The evaluation of opportunities, as outlined in Table 11, indicates that O3 (Opportunities for integration with hearing aids and other assistive technologies to enhance user experience) ranks highest with a score of 0.315437, signifying the increasing potential for technological integration and collaboration within the assistive listening sector. O4 (Expanding into over-the-counter hearing aid markets) ranks second, signifying substantial prospects for enhancing the accessibility and affordability of hearing solutions. O1 (Increasing demand for personalized, customizable hearing solutions) and O2 (Expanding senior population and market growth for assistive devices) are ranked third and fourth, respectively, indicating that although these trends are significant, they are less urgent than integration and market expansion opportunities. These findings underscore the necessity to leverage technical improvements and industry trends to foster growth and innovation.

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Table 11.

Opportunities evaluation and ranking.

	Sum	Product	Scores	Ranking
O1	0.33582	2.17E–32	0.16791	3
O2	0.397427	1.63E–31	0.198713	4
O3	0.630875	1.49E–28	0.315437	1
O4	0.590586	1.58E–29	0.295293	2

The threat assessment presented in Table 12 designates T4 (Regulatory barriers for over-the-counter hearing aids and market constraints inhibiting wider adoption) as the paramount threat, achieving the highest rating with a score of 0.356739. This highlights the difficulties presented by regulatory obstacles in broadening market access. T5 (Price sensitivity within the target demographic) ranks second, highlighting the necessity to reconcile cost with sophisticated features. T3 (Competing goods providing analogous features at reduced prices) and T2 (Reluctance to embrace new technology among users familiar with conventional hearing aids or simpler devices) are ranked third and fourth, respectively, underscoring the competitive and behavioral obstacles in the market. T1 (Intense competition from conventional hearing aids and sophisticated specialized assistive listening devices) ranks fifth, signifying that although competition is a concern, it is less paramount than regulatory and pricing challenges. These findings underscore the necessity of navigating regulatory frameworks and addressing consumer affordability to successfully reduce threats.

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Table 12.

Threats evaluation and ranking.

	Sum	Product	Scores	Ranking
T1	0.384552	2.25E–31	0.192276	5
T2	0.428512	1.24E–30	0.214256	4
T3	0.501962	6.97E–30	0.250981	3
T4	0.713478	9.77E–28	0.356739	1
T5	0.535453	6.77E–30	0.267726	2

Utilize the fuzzy COCOSO methodology to systematically rank the SWOT components for clear and effective strategic decision-making. Stakeholders can improve product offers, market positioning, and growth in the competitive environment of assistive listening devices by emphasizing strengths, fixing weaknesses, capitalizing on opportunities, and minimizing threats.

TOWS matrix: Strategy development

The TOWS matrix is a strategic instrument employed to synchronize internal factors (Strengths and Weaknesses) with external factors (Opportunities and Threats) to formulate actionable strategies. This chart displays an enhanced TOWS matrix that integrates all SWOT elements, emphasizing eight principal strategies for clarity and precision. Each strategy aims to exploit strengths, rectify flaws, seize opportunities, and alleviate dangers, guaranteeing focused and efficient results for headphone models in a competitive marketplace.

Table 13 presents a detailed TOWS matrix, classifying strategies into four quadrants: SO (Strengths-Opportunities), WO (Weaknesses-Opportunities), ST (Strengths-Threats), and WT (Weaknesses-Threats). It encompasses eight strategies targeting essential domains, including customized hearing solutions, integration with assistive technology, competition from conventional hearing aids, and price sensitivity. For instance, SO1 utilizes superior sound quality and distinctive characteristics to fulfill the need for customized solutions, whilst WT2 reduces expenses by offering economical versions. The table presents a definitive framework for stakeholders to augment product offerings, refine market positioning, and propel growth efficiently.

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Table 13.

TOWS matrix: strategic development for headphone models incorporating All SWOT factors.

TOWS strategies		Strengths (S)		Weaknesses (W)
Opportunities (O)		SO strategies		WO strategies
		(Maxi-Maxi): Leverage strengths to capitalize on opportunities.		(Mini-Maxi): Address weaknesses by exploiting opportunities.
O1: Rising demand for personalized hearing solutions.	SO1	Use S1 (Advanced sound quality) and S2 (Specialized hearing-impaired features) to develop customizable solutions tailored to individual hearing needs.	WO1	Improve W1 (Shorter battery life) to ensure compatibility with all-day-use scenarios in integrated systems.
O3: Integration with hearing aids and assistive technologies.	SO2	Leverage S2 (Bone conduction, speech clarity) and S4 (Extended battery life) to create seamless integrations with existing assistive devices.	WO2	Address W3 (Limited versatility—mainly designed for TV/media use or as hearing aids) by broadening product capabilities to serve diverse user applications, including general audio use, thereby appealing to a wider audience and reducing niche dependency.
Threats (T)		ST strategies		WT strategies
		(Maxi-Mini): Use strengths to mitigate threats.		(Mini-Mini): Minimize weaknesses to avoid threats.
T1: Intense competition from hearing aids.	ST1	Highlight S1 (Advanced sound customization) and S3 (Long wireless range) as unique selling points to differentiate from traditional hearing aids.	WT1	Address W3 (Limited versatility) by expanding product functionality to serve both assistive and general audio markets.
T5: Price sensitivity limiting access.	ST2	Emphasize S4 (Extended battery life) as a cost-saving feature, reducing long-term expenses for users.	WT2	Mitigate W2 (High cost) by introducing budget-friendly models with essential features for price-sensitive consumers.

Table 14 delineates the 16 most significant combined strategies extracted from a total of 72 potential combinations identified through the TOWS study. These strategies aim to exploit strengths, rectify deficiencies, seize opportunities, and alleviate threats concerning headphone models for hearing-impaired individuals and general customers. Each plan is delineated into precise steps, guaranteeing clarity and practical insights for stakeholders. This table functions as a thorough reference for the effective implementation of initiatives.

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Table 14.

Description of the combined strategies.

Strategy combination	Description
SO1 + SO2 + ST1 + ST2	Develop customizable hearing solutions using advanced sound quality (S1) and specialized features (S2). Integrate bone conduction (S2) and extended battery life (S4). Highlight long wireless range (S3) and advanced sound customization (S1) to differentiate from competitors. Emphasize extended battery life (S4) as a cost-saving benefit.
SO1 + SO2 + WO1 + WO2	Leverage advanced sound quality (S1) and specialized features (S2) for personalized hearing solutions. Improve battery life (W1) for all-day use. Broaden product versatility (W3) to serve diverse user applications.
SO1 + SO2 + WT1 + WT2	Use advanced sound quality (S1) and specialized features (S2) to develop customizable solutions. Expand product functionality (W3) for broader markets. Launch affordable models (W2) to capture price-sensitive segments.
SO1 + ST1 + WO1 + WT1	Develop customizable hearing solutions using advanced sound quality (S1) and specialized features (S2). Highlight long wireless range (S3) to differentiate from competitors. Improve battery life (W1) and broaden product versatility (W3).
SO1 + ST2 + WO1 + WT2	Leverage advanced sound quality (S1) and specialized features (S2) for personalized solutions. Emphasize extended battery life (S4) as a cost-saving benefit. Improve battery life (W1) and introduce affordable models (W2).
SO2 + ST1 + WO2 + WT1	Integrate bone conduction (S2) and extended battery life (S4) with assistive technologies. Highlight long wireless range (S3) to differentiate from competitors. Broaden product versatility (W3) and expand functionality for broader markets.
SO2 + ST2 + WO2 + WT2	Leverage bone conduction (S2) and extended battery life (S4) for integration with assistive technologies. Address limited versatility (W3) by broadening product capabilities. Launch affordable models (W2) for price-sensitive segments.
ST1 + ST2 + WT1 + WT2	Highlight advanced sound customization (S1) and long wireless range (S3) as unique selling points. Emphasize extended battery life (S4) as a cost-saving feature. Broaden product versatility (W3) and introduce affordable models (W2).
SO1 + SO2 + WO1 + WT1	Develop customizable hearing solutions using advanced sound quality (S1) and specialized features (S2). Improve battery life (W1) and expand product functionality (W3) to reduce niche dependency.
SO1 + SO2 + WO2 + WT2	Leverage advanced sound quality (S1) and specialized features (S2) for personalized solutions. Broaden product versatility (W3) and launch affordable models (W2) for price-sensitive segments.
SO1 + ST1 + WO2 + WT2	Use advanced sound quality (S1) and specialized features (S2) to develop customizable solutions. Highlight long wireless range (S3) to differentiate from competitors. Broaden product versatility (W3) and introduce affordable models (W2).
SO2 + ST1 + WO1 + WT2	Integrate bone conduction (S2) and extended battery life (S4) with assistive technologies. Highlight long wireless range (S3) to differentiate from competitors. Improve battery life (W1) and launch affordable models (W2).
SO1 + ST2 + WO2 + WT1	Leverage advanced sound quality (S1) and specialized features (S2) for personalized solutions. Emphasize extended battery life (S4) as a cost-saving benefit. Broaden product versatility (W3) and expand functionality for broader markets.
SO2 + ST2 + WO1 + WT1	Integrate bone conduction (S2) and extended battery life (S4) with assistive technologies. Emphasize extended battery life (S4) as a cost-saving benefit. Improve battery life (W1) and broaden product versatility (W3).
SO1 + SO2 + ST1 + WT1	Develop customizable hearing solutions using advanced sound quality (S1) and specialized features (S2). Highlight long wireless range (S3) to differentiate from competitors. Expand product functionality (W3) for broader markets.
SO1 + SO2 + ST2 + WT2	Leverage advanced sound quality (S1) and specialized features (S2) for personalized solutions. Emphasize extended battery life (S4) as a cost-saving benefit. Launch affordable models (W2) for price-sensitive segments.

Table 15 illustrates the Utility Matrix for Strategy Combinations. Experts assigned a weight to each technique, indicating its relative significance. The weights for the strategy codes are located in the second row of Table 15. These weights were employed to rank the strategies and guarantee that higher-priority options were identified.

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Table 15.

Fuzzy utility matrix for the 16 most important combined strategies derived from TOWS analysis.

Strategies included	Fuzzy utility (SO1)	Fuzzy utility (SO2)	Fuzzy utility (ST1)	Fuzzy utility (ST2)	Fuzzy utility (WO1)	Fuzzy utility (WO2)	Fuzzy utility (WT1)	Fuzzy utility (WT2)
	0.22	0.2	0.16	0.12	0.1	0.08	0.07	0.05
SO1 + SO2 + ST1 + ST2	(8.5, 9.0, 9.5)	(9.0, 9.5, 10.0)	(8.0, 8.5, 9.0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)
SO1 + SO2 + WO1 + WO2	(8.0, 8.5, 9.0)	(8.5, 9.0, 9.5)	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(0, 0, 0)
SO1 + SO2 + WT1 + WT2	(8.0, 8.5, 9.0)	(0, 0, 0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(6.5, 7.0, 7.5)	(0, 0, 0)	(6.0, 6.5, 7.0)	(6.5, 7.0, 7.5)
SO1 + ST1 + WO1 + WT1	(0, 0, 0)	(8.0, 8.5, 9.0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)
SO1 + ST2 + WO1 + WT2	(0, 0, 0)	(0, 0, 0)	(7.5, 8.0, 8.5)	(7.0, 7.5, 8.0)	(6.5, 7.0, 7.5)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.0, 6.5, 7.0)
SO2 + ST1 + WO2 + WT1	(8.0, 8.5, 9.0)	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)
SO2 + ST2 + WO2 + WT2	(0, 0, 0)	(8.0, 8.5, 9.0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.0, 6.5, 7.0)
ST1 + ST2 + WT1 + WT2	(7.5, 8.0, 8.5)	(8.0, 8.5, 9.0)	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)
SO1 + SO2 + WO1 + WT1	(0, 0, 0)	(0, 0, 0)	(7.5, 8.0, 8.5)	(7.0, 7.5, 8.0)	(0, 0, 0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)
SO1 + SO2 + WO2 + WT2	(7.5, 8.0, 8.5)	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)
SO1 + ST1 + WO2 + WT2	(0, 0, 0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.0, 6.5, 7.0)
SO2 + ST1 + WO1 + WT2	(7.5, 8.0, 8.5)	(8.0, 8.5, 9.0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(0, 0, 0)	(0, 0, 0)	(6.0, 6.5, 7.0)
SO1 + ST2 + WO2 + WT1	(0, 0, 0)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)	(5.5, 6.0, 6.5)
SO2 + ST2 + WO1 + WT1	(0, 0, 0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(7.0, 7.5, 8.0)	(6.5, 7.0, 7.5)	(0, 0, 0)	(0, 0, 0)	(6.0, 6.5, 7.0)
SO1 + SO2 + ST1 + WT1	(7.5, 8.0, 8.5)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(0, 0, 0)	(6.0, 6.5, 7.0)
SO1 + SO2 + ST2 + WT2	(0, 0, 0)	(7.5, 8.0, 8.5)	(0, 0, 0)	(7.0, 7.5, 8.0)	(0, 0, 0)	(0, 0, 0)	(6.5, 7.0, 7.5)	(6.0, 6.5, 7.0)

The Fuzzy Utility Matrix was developed to assess the efficacy of each integrated strategy. SO1 + SO2+ ST1 + ST2 possesses fuzzy utility values of (8.5, 9.0, 9.5) for SO1, (9.0, 9.5, 10.0) for SO2, and so on. These figures indicate the anticipated efficacy of the strategy combination across various scenarios.

Subsequently, the Zero-Sum Game approach was employed to rank and assess the 16 integrated methods.

This approach involves two players:

Table 16 displays the outcomes of employing the fuzzy Zero-Sum Game approach to assess and prioritize the 16 most significant combined strategies obtained from the TOWS research. Each strategy receives a score reflecting its performance within the Zero-Sum Game framework, and these scores are utilized to establish the ranking of the strategies. The scores indicate the strategies’ capacity to enhance strengths, rectify flaws, exploit opportunities, and alleviate risks, so offering a definitive prioritization for decision-making. This table is a vital result of the analysis, assisting stakeholders in choosing the most efficient ways for execution.

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Table 16.

Ranking of combined strategies based on fuzzy Zero-Sum Game analysis.

Strategies Included	Scores	Rank
SO1 + SO2 + ST1 + ST2	6.2	1
SO1 + SO2 + WO1 + WO2	5.06	3
SO1 + SO2 + WT1 + WT2	4.655	4
SO1 + ST1 + WO1 + WT1	4.015	7
SO1 + ST2 + WO1 + WT2	3.805	10
SO2 + ST1 + WO2 + WT1	3.435	12
SO2 + ST2 + WO2 + WT2	3.825	9
ST1 + ST2 + WT1 + WT2	4.275	5
SO1 + SO2 + WO1 + WT1	2.995	15
SO1 + SO2 + WO2 + WT2	4.225	6
SO1 + ST1 + WO2 + WT2	3.275	14
SO2 + ST1 + WO1 + WT2	5.685	2
SO1 + ST2 + WO2 + WT1	2.515	16
SO2 + ST2 + WO1 + WT1	3.525	11
SO1 + SO2 + ST1 + WT1	3.845	8
SO1 + SO2 + ST2 + WT2	3.315	13

Table 16 illustrates the rank of the examined strategies: The strategy SO1 + SO2 + ST1 + ST2 scores highest with a score of 6.2, demonstrating its exceptional efficacy in capitalizing on strengths and opportunities while alleviating dangers. This amalgamation integrates superior sound quality (SO1), tailored functionalities for hearing-impaired individuals (SO2), competitive differentiation (ST1), and cost-efficiency (ST2), rendering it the most efficacious method overall. Likewise, SO2 + ST1 + WO1 + WT2 ranks second with a score of 5.685, underscoring its robust emphasis on amalgamating strengths with opportunities while mitigating weaknesses to reduce threats. These premier strategies are strongly advised for prompt execution owing to their significant influence and congruence with business objectives.

The Mid-Ranked Strategies, including SO1 + SO2 + WO1 + WO2 (rank 3, score 5.06) and ST1 + ST2 + WT1 + WT2 (rank 5, score 4.275), exhibit moderate performance. These strategies concentrate on mitigating weaknesses and using strengths alongside opportunities; nonetheless, they are less effective than the highest-ranked tactics. For instance, SO1 + SO2 + WO1 + WO2 enhances battery longevity (WO1) and expands product variety (WO2), which are significant but not as vital as optimizing advanced sound quality and specialized features. These strategies ought to be regarded for execution as secondary priority.

The Lower-Ranked Strategies include: SO1 + ST2 + WO2 + WT1 (rank 16, score 2.515) and SO1 + SO2 + WO1 + WT1 (rank 15, score 2.995), which are positioned at the lowest tier, signifying their restricted efficacy. These combinations concentrate on mitigating weaknesses and reducing threats but lack the robust alignment with strengths and opportunities shown in superior plans. Although these strategies may have some merit, they ought to be deprioritized in favor of more consequential alternatives.

Hence, we must prioritize the highest-ranked strategies, specifically SO1 + SO2 + ST1 + ST2 and SO2 + ST1 + WO1 + WT2, as they have the greatest impact and alignment with company objectives.

Furthermore, we must see Mid-Ranked Strategies as Secondary Priorities: Strategies such as SO1 + SO2 + WO1 + WO2 and ST1 + ST2 + WT1 + WT2 should be executed as secondary priorities to tackle supplementary areas for enhancement.

Additionally, we deprioritize lower-ranked strategies: Strategies such as SO1 + ST2 + WO2 + WT1 and SO1 + SO2 + WO1 + WT1 should be deprioritized due to their minimal impact relative to higher-ranked alternatives.

The findings from the Zero-Sum Game analysis yield a definitive and practical ranking of the 16 integrated strategies. By concentrating on the highest-ranked strategies, stakeholders can optimize the efficacy of their strategic initiatives, guaranteeing congruence with organizational objectives and priorities. This method guarantees an equitable and rational distribution of resources, fostering growth and competitive superiority.