An Interval-Valued Neutrosophic Framework: Improved VIKOR with a Preference-Aware AHP–Entropy Weight Method for Evaluating Scalp-Detection Algorithms

Abstract

Scalp image detection faces challenges such as limited evaluation dimensions, difficulties in quantifying user perception, and insufficient discriminative power of traditional assessment methods. To address these issues, this paper proposes a multi-attribute decision-making model for deep learning algorithm selection. The model integrates subjective and objective weighting through a hybrid approach, where natural language processing (NLP) techniques extract perceptual preferences from user reviews, and the Interval-valued neutrosophic set analytic hierarchy process (IVNS-AHP) and entropy weight method (EWM) are employed to determine subjective and objective weights, respectively. The combined weights are used within the IVNS-VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) framework, enhanced by a possibility distribution (PD) to improve discriminative capability. Experiments were conducted using multiple performance metrics, including Precision, Recall, mean Average Precision at IoU = 0.5 (mAP@50), F1 Score, frames per second (FPS), and Parameters, to evaluate mainstream scalp detection algorithms. The results demonstrate that YOLOv8n achieves the highest comprehensive ranking with strong stability across different decision preferences. Comparative analyses with TODIM (an acronym in Portuguese of interactive and multiple attribute decision-making), TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), and fuzzy VIKOR variants confirm that the proposed PD-VIKOR method provides superior ranking stability and discriminative precision, offering a more reliable and robust evaluation under uncertainty.

1. Introduction

1.1. Background

Driven by national strategies such as the “Healthy China 2030” Outline and the “14th Five-Year Plan for National Health Informatization,” the concept of “comprehensive health” is profoundly reshaping public health management models in China, propelling a shift from passive treatment to proactive monitoring and self-management [1,2]. This trend has accelerated the development of smart health monitoring devices that integrate physiological sensing with artificial intelligence. Among these, the scalp health monitor stands out as a tool for personalized health care. Its core technology lies in analyzing scalp images to achieve precise quantification of physiological states and identification of pathological features.

As public health literacy improves, users’ demands for devices have moved beyond basic functionality, shifting instead to a greater focus on core performance metrics such as detection accuracy, response speed, ease of operation, and personalized service capabilities [3]. In the field of light medical aesthetics, such as scalp analyzers, “user experience first” has replaced single precision metrics as the new standard for evaluating device efficacy [4]. This shift demands multidimensional optimization in product design and drives algorithm selection away from pursuing “single-performance optimization” toward systematic decision-making based on “multidimensional user satisfaction” [5].

Product algorithm selection is fundamentally a multi-attribute group decision-making (MAGDM) problem, whose core lies in coordinating group decision-makers and comprehensively balancing multidimensional technical metrics with user subjective perceptions [6,7]. However, traditional decision-making models struggle to effectively address the widespread subjective ambiguity, scoring uncertainty, and group cognitive conflicts inherent in such decisions [8,9,10]. Therefore, how to construct a comprehensive evaluation framework that scientifically balances technical performance and user experience has become a critical issue requiring urgent resolution in this field.

1.2. Literature Review

In recent years, with the rapid increase of user-generated content and the advancement of artificial intelligence technologies, Natural language processing (NLP) methods, particularly text mining and sentiment analysis, have been increasingly applied in multi-attribute decision support systems. Compared with traditional survey-based approaches that rely on structured questionnaires or interviews, these techniques are widely recognized for their ability to extract authentic and real-time user preferences directly from large volumes of unstructured data [11]. For example, Zheng et al. [12] developed a sentiment interpretation model based on the Circular Pythagorean Fuzzy Set to optimize deep learning structure decisions, demonstrating the feasibility of transforming user reviews into effective decision inputs. Similarly, Yadav et al. [13] embedded sentiment scores extracted from online reviews into AHP-VIKOR and IF-MOORA models to comprehensively rank mobile payment platforms, thereby validating the adaptability of user semantic information in multi-criteria evaluation. However, despite these attempts to incorporate user sentiment into decision-making, existing studies still lack quantitative mechanisms derived from actual semantic feedback, which limits the realization of a truly user-centered model orientation [14]. Furthermore, many approaches continue to rely on traditional fuzzy set or intuitionistic fuzzy set theories, which may lead to semantic distortion and dimensional compression when representing user hesitation and emotional fluctuation [15], thus constraining the model’s capability to accommodate heterogeneous and multi-source information.

Previous studies have attempted to enhance the adaptability of decision-making models under uncertainty by extending fuzzy set theories, particularly in the integration of multi-source heterogeneous information and the representation of expert hesitation in scoring. Zhang et al. [16] addressed the product ranking problem of large-scale online reviews on e-commerce platforms by incorporating prospect theory into the VIKOR framework and developing a novel sentiment analysis algorithm. This approach strengthened the influence of user emotions on satisfaction computation while introducing a hybrid weighting mechanism that combines collective entropy weights with individual subjective preferences. Although this method effectively improved the personalization and dynamism of consumer satisfaction modeling, it still required explicit control over membership adjustment and exhibited limited capability in representing rating fuzziness and hesitation. Alamoodi et al. [17] constructed a two-stage weighting–ranking model (NS-FWZIC and NS-FDOSM) within a neutrosophic set environment for intelligent tourism recommendation systems. By managing the fluctuation of expert cognition, their approach achieved evaluation stability across heterogeneous application domains. However, the neutrosophic set adopted in their model was a simplified form, which failed to fully capture the coexistence of “support–opposition–hesitation” semantics in non-complementary cognitive structures, thereby constraining its generalization ability in complex opinion fusion scenarios.

As a generalized extension of fuzzy set theory, the IVNS models truth-membership, falsity-membership, and indeterminacy-membership as three independent functions, effectively overcoming the limitation of single-dimensional representation in traditional fuzzy sets. Unlike fuzzy sets and intuitionistic fuzzy sets, IVNS allows these three cognitive components to vary independently within the interval [0, 1] without satisfying any complementary constraint. This feature enables IVNS to represent evaluative attitudes under complex cognitive conditions more realistically, such as situations where “partial agreement,” “partial disagreement,” and “indecisiveness” coexist [18]. With these advantages, IVNS provides greater flexibility and interpretability when dealing with conflicting expert opinions, vague user evaluations, and incomplete information. In practical applications, IVNS has been extended into several variants, including weighted, probabilistic, and hesitant formulations. Zhang et al. [19] addressed the MAGDM requirements for agricultural B2C e-commerce service quality by proposing a “CRITIC weighting and IVIFS-GRA” framework, which effectively ranked and optimized service alternatives. Numerical and comparative experiments confirmed its validity and provided a feasible assessment approach for this field. Liu et al. [20] developed a hybrid MAGDM model under the IVIFS environment by integrating the IVIFWA aggregation operator, correlation-based expert weighting, and variable attribute weighting within a TOPSIS framework. Two numerical examples demonstrated its higher effectiveness and more stable ranking performance compared with traditional methods. Similarly, Zhou et al. [21] proposed a regional sustainability assessment model for the water–land–energy–carbon (WLEC) coupling system based on IVIFS and MAGDM. The application to Heilongjiang Province revealed notable intercity differences in coupling levels and yielded policy recommendations suggesting that groundwater utilization rates should be maintained within the range of 16% to 28%.

To further enhance the applicability of IVNS in the ranking stage of MAGDM, researchers have integrated it with improved VIKOR methods, particularly by incorporating possibility theory to strengthen the ranking capability under highly uncertain or hesitant information. Wang et al. [22] proposed a VIKOR method under a circular intuitionistic fuzzy (C-IF) environment by introducing an enhanced score function and a modified Chebyshev distance, which jointly characterize membership, non-membership, and information reliability while integrating radial features. The method achieved more robust superiority identification and compromise ranking in a medical waste disposal case. Hendiani et al. [23] developed a VIKOR model based on the interval-valued q-rung orthopair fuzzy set (IVq-ROFS) using a dual-layer possibility and neutralized decision matrix. This approach eliminated the need for conventional normalization and calculated utility and compromise measures through cumulative possibility–weight interactions, yielding a unique and distinguishable ranking with higher robustness in group decision contexts. Chen et al. [24] addressed the issues of zero-radius failure and semantic loss in the relative scoring of C-IF VIKOR by proposing a new score function with scale and exponential parameters, coupled with a C-IF Minkowski distance to form a parameterized VIKOR model. This model flexibly balanced utility, regret, and compromise effects, and demonstrated strong adaptability and stability in applications such as site selection, supplier evaluation, and medical waste technology assessment.

1.3. Research Gap

The significance of intelligent health monitoring devices and image analysis algorithms has become increasingly prominent. However, most existing studies primarily focus on single-dimensional comparisons of algorithmic performance, such as improving recognition accuracy or optimizing computational complexity [25], while lacking a systematic and integrative evaluation framework that simultaneously incorporates algorithmic technical attributes and end-user perceptual dimensions.

Specifically, the limitations of current research can be summarized in three aspects.

(1)

From a methodological perspective, there is an absence of mature theoretical models capable of effectively addressing the inherent subjectivity, uncertainty, and group divergence in algorithm selection processes.

(2)

From a research perspective, algorithms are often treated merely as technical entities, neglecting their role as components of user-oriented products. This results in a disconnection between technical performance indicators and user satisfaction.

(3)

From an interdisciplinary application perspective, the systematic application of advanced fuzzy theoretical frameworks such as the IVNS to image detection algorithm evaluation remains largely unexplored [26]. This gap between theoretical development and practical implementation highlights the necessity and innovative value of the present study.

1.4. Research Contributions

In response to the existing limitations in methodology, research perspective, and interdisciplinary application, the contributions of this paper are reflected in three main aspects.

(1)

From a methodological standpoint, this paper integrates the AHP with the VIKOR method and extends it to the IVNS environment. Two types of possibility functions are further defined to enhance the VIKOR mechanism, significantly improving the precision of alternative comparison and the discriminative power of ranking. This provides a more robust theoretical tool for addressing the complex cognitive uncertainty inherent in algorithm selection.

(2)

From the perspective of research orientation, this paper introduces NLP techniques to construct a user-preference-oriented hybrid weighting approach that combines subjective and objective information. By structurally integrating multidimensional user experience indicators, the proposed framework shifts the decision-making focus from “technically optimal” to “user-satisfactory,” effectively bridging the gap between technical performance metrics and actual user perception.

(3)

From an interdisciplinary application perspective, this paper applies IVNS theory to the evaluation and selection of image detection algorithms for the first time. This work not only extends the application boundary of fuzzy decision-making theory but also provides a novel theoretical reference for the development of intelligent health terminal products that integrate both technical performance and user preference.

1.5. Organization

The remainder of this paper is structured as follows: Section 2 reviews text mining techniques and sentiment analysis methods in natural language processing, along with IVNS-related operations. Section 3 details the steps of the proposed method. Section 4 presents empirical research on this approach. Section 5 conducts sensitivity analysis and compares the proposed method with other approaches. Section 6 discusses the results.

2. Preliminaries

2.1. User Requirement Identification and Weighting Construction

2.1.1. TF-IDF (Term Frequency-Inverse Document Frequency) Weighting Technique

User review data was collected via web crawlers. Preprocessing steps included word segmentation, stopword removal, word frequency counting, and TF-IDF calculation (see [27,28]).

Term frequency (TF):

$$TF(t,d)={\displaystyle \frac{\mathrm{n}}{N}}$$

(1)

where t represents a specific word, d represents the number of documents, n is the frequency of that term within the documents, and N is the total number of words in the documents.

TF-IDF:

$$TF\text{-}IDF(t,d)=TF(t,d)\times \log {\displaystyle \frac{D}{1+\mathrm{d}f(t)}}$$

(2)

where D is the total number of documents in the corpus, and $d{f}_t$ is the number of documents containing term t.

2.1.2. LDA Topic Identification and Visualization

The Latent Dirichlet Allocation (LDA) model was employed for topic modeling [29], with its structural framework illustrated in Figure 1. The optimal number of topics was determined using perplexity and topic consistency:

Perplexity (see [30]):

$$Perplexity(D)=\exp (-{\displaystyle \frac{{\displaystyle {\sum }_{d\in D}\log P(w_d)}}{{\displaystyle {\sum }_{d\in D}{N}_d}}})$$

(3)

where $P\left(w_d\right)$ is the joint probability of all words in document d, $N_d$ denotes the number of words in document d, ${\sum }_{d\in D}{N}_d$ is the total number of words across all documents.

Thematic Consistency (see [31]):

$$C(W)={\displaystyle \sum _{j=2}^M{\displaystyle \sum _{i=1}^{j-1}\log }}{\displaystyle \frac{D(w_i,w_j)+1/\epsilon }{D(w_i)}}$$

(4)

where $D\left(w_i\right)$ denotes the number of documents containing, $D(w_i,w_j)$ is the number of documents containing both $w_i$ and $w_j$, and $1/\epsilon$ is the smoothing factor.

2.1.3. User Preference Weighting

To enhance the accuracy and domain adaptability of sentiment recognition, this paper utilizes Baidu’s NLP sentiment analysis API to process user review texts. The specific processing steps are outlined in Algorithm 1.

Algorithm 1: Sentiment Analysis Using Baidu NLP API

Input: Text content, API Key, Secret Key

Output: Sentiment polarity and confidence score

Step 1: Authenticate with Baidu OAuth server using API Key and Secret Key

Step 2: Obtain access_token from the response

Step 3: Construct request URL with access_token

Step 4: Create JSON payload with the input text

Step 5: Send HTTP POST request to the sentiment_classify endpoint

Step 6: Parse JSON response

Step 7: Extract:

→ sentiment ∈ {0: Negative, 1: Neutral, 2: Positive}

→ confidence ∈ [0, 1]

→ positive_prob, negative_prob

Step 8: Return sentiment result for further processing

Calculate the user’s preference score for the metric $t_j$:

$$S_j={\displaystyle \frac{1}{n_j}}{\displaystyle \sum _{i=1}^{n_j}(\frac{e_{ij}+1}{3}\cdot {\gamma }_{ij})}$$

(5)

where $n_j$ represents the total number of comments related to indicator $t_j$, $e_{ij}\in \left\{0,1,2\right\}$ represents emotional polarity, corresponding to negative, neutral, and positive, respectively, ${\gamma }_{ij}\in \left[0,1\right]$ represents the sentiment classification confidence score output by Baidu’s NLP model.

Normalized User Preference Weight:

$$w_j^{user}={\displaystyle \frac{S_j-\min (S)}{{\displaystyle {\sum }_{k=1}^K(S_k-\min (S))}}}$$

(6)

2.2. IVNS-Related Operations

Definition 1

(see [32]). Let X denote a non-empty domain. An IVNS $\tilde{N}$ is defined by a ternary membership function.

$$\tilde{N}=\left\{〈x,T_N(x),I_N(x),F_N(x)〉|x\in X\right\}$$

(7)

Here,

• $T_N\left(x\right)=\left[T_N^L\left(x\right),T_N^U\left(x\right)\right]$ Indicates the true membership interval of element x belonging to set $\tilde{N}$;
• $I_N\left(x\right)=\left[I_N^L\left(x\right),I_N^U\left(x\right)\right]$ Indicates the uncertain membership interval of element x belonging to set $\tilde{N}$;
• $F_N\left(x\right)=\left[F_N^L\left(x\right),F_N^U\left(x\right)\right]$ Indicates the false membership interval of element x belonging to set $\tilde{N}$;

and satisfy

$$0\le \rho ,\sigma ,\tau \le 1,\rho \in T_N(x),\sigma \in I_N(x),\tau \in F_N(x)$$

(8)

$$0\le \sup T_N(x)+\sup I_N(x),+\sup F_N(x)\le 3$$

(9)

Definition 2

(see [33]). Let $\tilde{N}$ denote an IVNS in X. The IVNS  $\tilde{N}$ is defined as

$$\tilde{N}=\left\{〈x,\left[T_N^L(x),T_N^U(x)\right],\left[I_N^L(x),I_N^U(x)\right],\left[F_N^L(x),F_N^U(x)\right]〉|x\in X\right\}$$

(10)

Here,

• $T_N^L\left(x\right)$ and $T_N^U\left(x\right)$ denote the lower bound and upper bound of the true membership degree interval, respectively;
• $I_N^L\left(x\right)$ and $I_N^U\left(x\right)$ denote the lower and upper bounds of the uncertainty membership interval, respectively;
• $F_N^L\left(x\right)$ and $F_N^U\left(x\right)$ denote the lower bound and upper bound of the pseudo-membership interval, respectively.

Definition 3

(see [34]). Defuzzify an IVNS

$$\Omega (x)=\left({\displaystyle \frac{T_N^L(x)+T_N^U(x)}{2}}+(I_N^U(x))\left(1-{\displaystyle \frac{I_N^L(x)+I_N^U(x)}{2}}\right)-\left(1-F_N^U(x)\right)\left({\displaystyle \frac{F_N^L(x)+F_N^U(x)}{2}}\right)\right)$$

(11)

3. Methods

This paper aims to construct an improved decision model for the comprehensive evaluation of scalp detection algorithms, with the specific workflow illustrated in Figure 2. This model integrates IVNS theory, AHP, and VIKOR methodology. Its weighting system comprises subjective and objective components: First, NLP technology analyzes web-crawled user review text data to quantify user preferences, then determines composite subjective weights using the IVNS-AHP method. Second, employ EWM to calculate the objective weighting of technical metrics for target detection algorithms. Finally, the subjective and objective weights are multiplied to obtain the final weight. During the evaluation phase, based on the improved IVNS-VIKOR method, comprehensive ranking of algorithm solutions is achieved by calculating group utility, individual regret, and compromise indicators.

3.1. IVNS-AHP Subjective Empowerment

The IVNS-AHP procedure is as follows [34]:

Step 1. Identify objectives, criteria, and factors for the scheme-level study.

Step 2. Construct the IVNS language evaluation scale for AHP weight calculation, as shown in

Table 1. IVNS language evaluation scale for AHP weight calculation.

Importance	Abbreviation	True Value Interval T	Uncertainty Interval I	False Value Range F
Equally important	EI	[0.50, 0.50]	[0.50, 0.50]	[0.50, 0.50]
Absolutely less important	AWI	[0.50, 0.60]	[0.35, 0.45]	[0.40, 0.50]
Extremely less important	EWI	[0.55, 0.65]	[0.30, 0.40]	[0.35, 0.45]
Less important	MWI	[0.60, 0.70]	[0.25, 0.35]	[0.30, 0.40]
Generally less important	GWI	[0.65, 0.75]	[0.20, 0.30]	[0.25, 0.35]
Generally important	GI	[0.70, 0.80]	[0.15, 0.25]	[0.20, 0.30]
Relatively important	MI	[0.75, 0.85]	[0.10, 0.20]	[0.15, 0.25]
Generally more important	GSI	[0.80, 0.90]	[0.05, 0.10]	[0.10, 0.20]
Relatively more important	MSI	[0.90, 0.95]	[0.00, 0.05]	[0.05, 0.15]
Extremely more important	ESI	[0.95, 1.0]	[0.00, 0.00]	[0.00, 0.10]
Absolutely more important	ASI	[1.0, 1.0]	[0.00, 0.00]	[0.00, 0.00]

.

Step 3. Construct a pairwise comparison matrix using the IVNS language evaluation scale.

$$IVN{S}_{ji}=IVN{S}_{ij}^{\mathrm{C}}=\left\{〈\left[F_{IVN{S}_{\mathrm{ij}}}^L,F_{IVN{S}_{\mathrm{ij}}}^U\right],\left[1-I_{IVN{S}_{\mathrm{ij}}}^U,1-I_{IVN{S}_{\mathrm{ij}}}^L\right],\left[T_{IVN{S}_{\mathrm{ij}}}^L,T_{IVN{S}_{\mathrm{ij}}}^U\right]〉\right\}$$

(12)

$${\tilde{A}}_{IVNS}=\left[\begin{array}{cccc}IVN{S}_{11}& IVN{S}_{12}& \dots & IVN{S}_{1n}\\ IVN{S}_{21}& IVN{S}_{22}& \dots & IVN{S}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ IVN{S}_{n1}& IVN{S}_{n2}& \dots & IVN{S}_{nn}\end{array}\right]$$

(13)

If the importance of factor $A_i$ relative to $B_j$ is $IVN{S}_{ij}$, The importance of $B_j$ relative to $A_i$ is determined by the symmetric equivalence class $IVN{S}_{ij}^C$. Additionally $IVN{S}_{ii}=⟨\left[0.50,0.50\right],\left[0.50,0.50\right],\left[0.50,0.50\right]⟩$ denotes the self-comparison item.

Step 4. The pairwise comparison matrix is deneutrosophicated using Equation (11) and subjected to a consistency check. If the deneutrosophicated pairwise comparison matrix passes the consistency test, then the consistency of the matrix constructed from the IVNS is considered to be validated.

$$\mathrm{CI}={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(14)

$$\mathrm{CR}={\displaystyle \frac{\mathrm{CI}}{\mathrm{RI}}}$$

(15)

where n denotes the order of the matrix; CI represents the consistency index; CR denotes the consistency ratio; RI indicates the random consistency index.

Step 5. Normalize the IVNS matrix and calculate the arithmetic mean of each row to obtain the interval-valued neutrosophic weighting for the indicator.

$$IVN{S}_{ij}=〈\left[{\displaystyle \frac{T_{ij}^L}{{\displaystyle \sum _{i=1}^n{T}_{ij}^U}}},{\displaystyle \frac{T_{ij}^U}{{\displaystyle \sum _{i=1}^n{T}_{ij}^U}}}\right],\left[{\displaystyle \frac{I_{ij}^L}{{\displaystyle \sum _{i=1}^n{I}_{ij}^U}}},{\displaystyle \frac{I_{ij}^U}{{\displaystyle \sum _{i=1}^n{I}_{ij}^U}}}\right],\left[{\displaystyle \frac{F_{ij}^L}{{\displaystyle \sum _{i=1}^n{F}_{ij}^U}}},{\displaystyle \frac{F_{ij}^U}{{\displaystyle \sum _{i=1}^n{F}_{ij}^U}}}\right]〉$$

(16)

$$w_j={\displaystyle \frac{{\displaystyle \sum _{i=1}^{n}IVN{S}_{ij}}}{n}}$$

(17)

Step 6. The weights are deneutrosophicated using Equation (11), and the IVNS-AHP weights $w_i^{\mathit{AHP}}$ are obtained.

Step 7. Calculate the subjective weights using a linear combination approach, with the specific calculation method as follows:

$$w_j^{subj}=\alpha w_j^{user}+(1-\alpha )w_j^{AHP}$$

(18)

where $w_j^{subj}$ denotes the composite subjective weight, $\alpha$ is set to 0.6 in this paper; see Section 5 for detailed discussion. $w_j^{user}$ represents the user preference weight, while $w_j^{AHP}$ signifies the IVNS-AHP subjective weight.

3.2. Objective Weighting Using the EWM

The specific steps of the EWM are as follows:

Step 1. Let there be m scalp-detection algorithms and n technical indicators. Collect the objective performance data for each algorithm with respect to each indicator, and construct the initial technical evaluation matrix $X$,

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(19)

where $x_{ij}$ represents the actual measurement value of the i-th algorithm on the j-th indicator.

Step 2. Standardize the data and construct the standardized evaluation matrix $Y$,

$$y_{ij}^{+}={\displaystyle \frac{x_{ij}-{\min }_i(x_{ij})}{{\max }_i(x_{ij})-{\min }_i(x_{ij})}},i=1,2,\dots ,m,j=1,2,\dots ,n$$

(20)

$$y_{ij}^{-}={\displaystyle \frac{{\max }_i(x_{ij})-x_{ij}}{{\max }_i(x_{ij})-{\min }_i(x_{ij})}},i=1,2,\dots ,m,j=1,2,\dots ,n$$

(21)

$$Y={(y_{ij})}_{m\times n},i=1,2,\dots ,m,j=1,2,\dots ,n$$

(22)

where $y_{ij}^{+}$ denotes benefit-oriented indicators, $y_{ij}^{-}$ denotes cost-oriented indicators, and ${\mathit{min}}_i(x_{ij})$ represents the minimum value among all algorithms under the j-th indicator.

Step 3. Calculate the adjustment coefficient, the information entropy of each indicator, and the corresponding weights.

$$p_{ij}={\displaystyle \frac{y_{ij}}{{\displaystyle \sum _{k=1}^m{\mathrm{y}}_{kj}}}}$$

(23)

$$H_j=-{\displaystyle \frac{1}{\ln m}}{\displaystyle \sum _{i=1}^m{p}_{ij}}\ln (p_{ij}),j=1,2,\dots n,H_j\ge 0$$

(24)

$$w_j^{tech}={\displaystyle \frac{1-H_j}{n-{\displaystyle \sum _{k=1}^n{H}_k}}}$$

(25)

where $p_{ij}$ denotes the normalization ratio, $H_j$ represents information entropy, and $w_j^{tech}$ indicates the objective weighting factor in the entropy weighting method.

3.3. Subjective-Objective Indicator Mapping

Due to the fuzziness and non-technical nature of user evaluation dimensions, it is difficult to establish a one-to-one correspondence with the quantifiable parameters observed during the actual operation of the algorithms. Therefore, a subjective–objective indicator mapping matrix needs to be constructed. Let the subjective indicator be denoted as $P=\left\{p_1,p_2,\dots p_k\right\}$ and the objective indicator as $Q=\left\{q_1,q_2,\dots q_m\right\}$. Construct the subjective-objective indicator mapping matrix $M={\left[m_{ij}\right]}_{k\times n}$, where each element $m_{ij}$ represents the mapping strength of subjective indicator $p_i$ to objective indicator $q_j$, i.e., the weight contribution. Thus, the mapping weight is

$$w_j^{map}=w_j^{subj}\cdot \mathrm{M}$$

(26)

where $w_j^{map}$ denotes the mapping weight, $w_j^{subj}$ represents the composite subjective weight, and M is the subjective-objective indicator mapping matrix.

3.4. Final Weighting of Indicators

This paper employs the multiplicative synthesis method to calculate the final weights of the indicators [35]:

$$w_j^{final}={\displaystyle \frac{w_j^{map}\cdot w_j^{tech}}{{\displaystyle \sum _{j=1}^n\left(w_j^{map}\cdot w_j^{tech}\right)}}}$$

(27)

where $w_j^{final}$ denotes the final weight, $w_j^{map}$ denotes the mapping weight, and $w_j^{tech}$ denotes the objective weight under the entropy weight method.

3.5. Improving the IVNS-VIKOR Comprehensive Evaluation

3.5.1. Constructing the IVNS Decision Matrix

Let the set of evaluation algorithms be $A=\left\{A_1,A_2,\dots A_m\right\}$, and the set of evaluation criteria be $C=\left\{C_1,C_2,\dots C_n\right\}$. An IVNS decision matrix $\tilde{X}={\left[x_{ij}\right]}_{m\times n}$ is constructed, where each evaluation value $x_{ij}$ of algorithm $A_i$ under criterion $C_j$ is represented by an interval-valued neutrosophic number in the following form:

$${\tilde{x}}_{ij}=〈\left[T_{ij}^L,T_{ij}^U\right],\left[I_{ij}^L,I_{ij}^U\right],\left[F_{ij}^L,F_{ij}^U\right]〉$$

(28)

where $T_{ij}$ denotes the degree of acceptance of algorithm $A_i$ under criterion $C_j$, $I_{ij}$ represents the degree of indeterminacy, and $F_{ij}$ represents the degree of falsity. According to the linguistic evaluation scale provided in

Table 2. IVNS language evaluation scale for VIKOR evaluation.

Importance	Abbreviation	True Value Interval T	Uncertainty Interval I	False Value Range F
Unable to determine	UT	[0.50, 0.50]	[0.50, 0.50]	[0.50, 0.50]
Extremely poor	VP	[0.50, 0.60]	[0.35, 0.45]	[0.40, 0.50]
Very poor	VHP	[0.55, 0.65]	[0.30, 0.40]	[0.35, 0.45]
Poor	MP	[0.60, 0.70]	[0.25, 0.35]	[0.30, 0.40]
Slightly poor	SP	[0.65, 0.75]	[0.20, 0.30]	[0.25, 0.35]
Average	F	[0.70, 0.80]	[0.15, 0.25]	[0.20, 0.30]
Slightly better	SG	[0.75, 0.85]	[0.10, 0.20]	[0.15, 0.25]
Better	MG	[0.80, 0.90]	[0.05, 0.10]	[0.10, 0.20]
Very good	VHG	[0.90, 0.95]	[0.00, 0.05]	[0.05, 0.15]
Excellent	VG	[0.95, 1.0]	[0.00, 0.00]	[0.00, 0.10]
Perfect	P	[1.0, 1.0]	[0.00, 0.00]	[0.00, 0.00]

, experts evaluate each algorithm, and the corresponding decision matrix is thereby constructed.

3.5.2. Determine the Positive and Negative Ideal Solutions

For benefit-type criteria, set the positive and negative ideal solutions as

$$\begin{array}{l}{\tilde{x}}_j^{+}=〈\left[T_j^{+L},T_j^{+U}\right],\left[I_j^{+L},I_j^{+U}\right],\left[F_j^{+L},F_j^{+U}\right]〉\\ =〈\left[\underset{i}{\max }{T}_{ij}^L,\underset{i}{\max }{T}_{ij}^U\right],\left[\underset{i}{\min }{I}_{ij}^L,\underset{i}{\min }{I}_{ij}^U\right],\left[\underset{i}{\min }{F}_{ij}^L,\underset{i}{\min }{F}_{ij}^U\right]〉\end{array}$$

(29)

$$\begin{array}{l}{\tilde{x}}_j^{-}=〈\left[T_j^{-L},T_j^{-U}\right],\left[I_j^{-L},I_j^{-U}\right],\left[F_j^{-L},F_j^{-U}\right]〉\\ =〈\left[\underset{i}{\min }{T}_{ij}^L,\underset{i}{\min }{T}_{ij}^U\right],\left[\underset{i}{\max }{I}_{ij}^L,\underset{i}{\max }{I}_{ij}^U\right],\left[\underset{i}{\max }{F}_{ij}^L,\underset{i}{\max }{F}_{ij}^U\right]〉\end{array}$$

(30)

For cost-type criteria, set the positive and negative ideal solutions as

$$\begin{array}{l}{\tilde{x}}_j^{+}=〈\left[T_j^{+L},T_j^{+U}\right],\left[I_j^{+L},I_j^{+U}\right],\left[F_j^{+L},F_j^{+U}\right]〉\\ =〈\left[\underset{i}{\min }{T}_{ij}^L,\underset{i}{\min }{T}_{ij}^U\right],\left[\underset{i}{\max }{I}_{ij}^L,\underset{i}{\max }{I}_{ij}^U\right],\left[\underset{i}{\max }{F}_{ij}^L,\underset{i}{\max }{F}_{ij}^U\right]〉\end{array}$$

(31)

$$\begin{array}{l}{\tilde{x}}_j^{-}=〈\left[T_j^{-L},T_j^{-U}\right],\left[I_j^{-L},I_j^{-U}\right],\left[F_j^{-L},F_j^{-U}\right]〉\\ =〈\left[\underset{i}{\max }{T}_{ij}^L,\underset{i}{\max }{T}_{ij}^U\right],\left[\underset{i}{\min }{I}_{ij}^L,\underset{i}{\min }{I}_{ij}^U\right],\left[\underset{i}{\min }{F}_{ij}^L,\underset{i}{\min }{F}_{ij}^U\right]〉\end{array}$$

(32)

3.5.3. Improved VIKOR Method

Inspired by reference [36], this paper extends the PD to the VIKOR method under the IVNS environment, and for the first time introduces an attribute-level possibility distribution (ALPD) based on the normalized difference in interval lengths. In addition, a ranking-level possibility distribution (RLPD) is defined to compare the possibility distributions of the compromise indicators, enabling finer-grained discrimination during the ranking stage. This improvement effectively enhances the model’s discriminative capability under approximate Q-value conditions and strengthens the precision and stability of the ranking results.

Step 1. Calculate the ALPD, defined by the following formula:

$$P({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+})=\max \left\{1-\max \left\{{\displaystyle \frac{{\gamma }_j^{U+}-T_{ij}^L}{L({\tilde{x}}_{ij})+L({\tilde{x}}_j^{+})}},0\right\},0\right\}$$

(33)

$${\gamma }_j^{U+}=T_j^{U+}+I_j^{U+}+F_j^{U+}$$

(34)

$$L(\tilde{x})=(T^U-T^L)+(I^U-I^L)+(F^U-F^L)$$

(35)

where $P({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+})$ represents the degree to which ${\tilde{x}}_{ij}$ is superior to the positive ideal solution, ${\gamma }_j^{U+}$ denotes the upper bound sum of the positive ideal solution interval, and $L\left(\tilde{x}\right)$ represents the length of the interval-valued neutrosophic number $\tilde{x}$.

Step 2. Using the ALPD calculated in Step 1, compute the population utility $S_i$ and individual regret $R_i$.

$$S_i={\displaystyle \sum _{j=1}^{\mathrm{n}}{w}_j^{final}}\cdot \left[1-({\displaystyle \frac{P({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+})-P_{\min }}{P_{\max }-P_{\min }}})\right]$$

(36)

$$R_i=\underset{j}{\max }\left\{w_j^{final}\cdot \left[1-({\displaystyle \frac{P({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+})-P_{\min }}{P_{\max }-P_{\min }}})\right]\right\}$$

(37)

where $w_j^{final}$ is the final weight of indicator $C_j$. $P_{max}=maxP\left({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+}\right)$ and $P_{min}=minP\left({\tilde{x}}_{ij}\ge {\tilde{x}}_j^{+}\right)$ represent the maximum and minimum possible values of all schemes under criterion $C_j$, respectively.

Step 3. Integrate group utility and individual regret to calculate the compromise index $Q_i$

$$Q_i=v{\displaystyle \frac{S_i-S_{\min }}{S_{\max }-{\mathrm{S}}_{\min }}}+(1-v){\displaystyle \frac{R_i-R_{\min }}{R_{\max }-R_{\min }}}$$

(38)

where $v\in \left[0,1\right]$ is the decision mechanism coefficient, $v$ is typically set to 0.5 to balance group utility and individual regret $S_{min}=min{S}_i$, $S_{max}=max{S}_i$.

Step 4. Calculate the RLPD, defined by the following formula:

$$P(Q_k\le Q_l)={\displaystyle \frac{\max (0,Q_l^U-Q_k^L)-\max (0,Q_k^L-Q_l^U)}{(Q_k^U-Q_k^L)+(Q_l^U-Q_l^L)}}$$

(39)

where $P(Q_k\le Q_l)$ denotes the probability that algorithm $A_k$ is not inferior to algorithm $A_l$ in a compromise sense. $Q_k^L$,$Q_k^U$,$Q_l^L$ and $Q_l^U$ represents the potential lower bound and upper bound of the compromise metric $Q$ for algorithms $A_k$ and $A_l$, respectively.

Based on the RLPD $P(Q_k\le Q_l)$ for every pair of alternatives, the evaluation algorithms are ultimately ranked according to $P(Q_k\le Q_l)>0.5$, and the ranking results are then aggregated. The formulas are as follows:

$$W_{\mathrm{k}}={\displaystyle \sum _{l\ne k}1\cdot \left[P(Q_k\le Q_l)>0.5\right]}$$

(40)

$${{\displaystyle \sum P}}_k={\displaystyle \sum _{l\ne k}\left[P(Q_k\le Q_l)\right]}$$

(41)

where $W_k$ denotes the number of pairwise comparisons won, and ${\sum P}_k$ represents the overall advantage score.

4. Empirical Research

4.1. User Requirement Weight Analysis

4.1.1. Data Sources and Preprocessing

This paper utilized JD.com, Tmall, Xiaohongshu, and Weibo as data source platforms. Keywords such as “scalp analyzer,” “scalp health monitor,” and “scalp care device” were employed for retrieval. Data collection was conducted using the Octopus Web Scraper software (version 8.7.7), yielding a total of 169,341 text data entries. The exported initial comment dataset included user nicknames, response timestamps, question titles, and answer content, as shown in Figure 3.

The collected Chinese textual data were preprocessed through word segmentation and stop-word removal. Subsequently, the term frequencies and TF-IDF values of the segmented words were calculated according to Equations (1) and (2), as presented in

Table 3. Keyword Frequency Statistics.

	Keyword	TF-IDF	Frequency
1	Report	0.400	1034
2	Effect	0.399	3945
3	Minutes	0.381	1953
4	Smart	0.380	1132
5	Precision	0.371	945
6	Detector	0.351	1734
7	Hair Loss	0.350	10,442
8	System	0.344	1239
9	Equipment	0.343	1826
10	Professional	0.338	2497
11	Follicle	0.334	11,504
12	Detection	0.332	8446
13	Oil	0.305	2256
14	Technology	0.280	2728
15	Scalp	0.262	21,312

.

To address the issues of broad semantics and weak specificity in high-frequency vocabulary within review texts, this paper employs the LDA topic model for deep semantic modeling. Prior to model training, TF-IDF is applied to weight and optimize text features, significantly improving LDA’s topic clustering effectiveness and enhancing the model’s ability to capture deep semantics [37]. The number of topics was set between 2 and 16. According to Formulas (3) and (4), the corresponding confusion and consistency scores for each topic were calculated. A line chart illustrating the variation in perplexity/consistency scores with the number of topics is presented in Figure 4.

Based on the evaluation results, selecting four topics as the optimal number strikes a reasonable balance between model performance and practical application needs [38,39]. Although its perplexity (41.81) and coherence score (0.48) do not reach the theoretical optimum, this number of topics substantially reduces model complexity, greatly improves computational efficiency, and avoids the semantic fragmentation caused by excessive topic granularity.

Inspired by [40], this paper further introduces Kullback–Leibler divergence (KLD) and Jensen–Shannon divergence (JSD) as auxiliary validation metrics to quantify the magnitude and stability of semantic structural changes under varying topic numbers. KLD measures the asymmetric difference between two probability distributions, whereas JSD, as its symmetric and smoothed extension, better captures the average semantic distance between topics, thereby reflecting changes in topic separability.

According to the divergence results between adjacent topic models (see Figure 5), when the number of topics increases from 3 to 4, the JSD rises to 0.4561, indicating enhanced semantic distinction and clearer topic boundaries. As the topic number further increases from 4 to 5, the JSD markedly rises to 0.5417, and the KLD (4.1548 and 4.1553) reach local peaks, suggesting that the model achieves its strongest semantic separation at this stage. This implies that four topics are sufficient to capture the dominant semantic space, and adding more topics may lead to excessive differentiation and redundant themes, thereby weakening overall interpretability.

In contrast, when the topic number increases from 5 to 6 and 6 to 7, the JSD slightly decreases (0.4874 and 0.4789), indicating a convergence of topic differences. At 7 to 8, the JSD further drops to 0.4166, implying that topic boundaries become blurred and model stability declines. Subsequently, during the 8 to 9 and 9 to 10 transitions, the JSD rises again, revealing a “semantic fluctuation–overlap” phenomenon, where newly generated topics partially overlap semantically with existing ones, thus reducing structural distinctiveness.

Based on the four themes identified from the preceding analysis, this paper employs the LDA topic modeling using the Gensim library (version 4.4.0) in Python (version 3.11) to analyze online text data. The visualization of the modeling results is implemented through the pyLDAvis library, and the topic clustering map is exported in HTML format (see Figure 6). In this visualization, each of the four bubbles represents a distinct topic, where the bubble size intuitively reflects the relative weight of that topic in the corpus, and the distance between bubbles quantifies the semantic similarity among topics—the closer the distance, the stronger the thematic correlation. The visualization results indicate that the LDA model achieves a clear and well-defined separation among topics.

This paper uses the LDA topic model to extract topics from online review texts and identifies four topic categories that reflect the needs of scalp detector users. The number of topics captures the multidimensional nature of user requirements, while the characteristic terms of each topic reveal its specific connotations. For each topic, we select the top 20 most frequent words as the core feature terms (see

Table 4. Subject categories and characteristic words.

	Theme Category	Theme Keywords
Topic#1	Functional Quality	Function, capability, efficacy, resolution, process, high efficiency, precision, accuracy, detector, durability, implementation, algorithm, robustness, analyzer, sensitivity, tester, hormone levels, high quality, stability, standardization
Topic#2	Product Experience	Recommendations, Operations, Feedback, Readability, Guidance, User-Friendly, Interface, Evaluation, Impression, Navigation, Aesthetics, Instructional, Exquisite, Service Attitude, Ease of Use, Consultant, Comfort Level, Service Center, Satisfaction, After-Sales Service
Topic#3	Human Factors Engineering Design	Adjustment, clarity, space, distance, intuitive, height, thickness, convenience, ergonomics, hand feel, personalization, definition, indications, easy to understand, design, multi-angle, handy, adjustability, visualization, close-up distance
Topic#4	Safety	Cleaning, inspection, safety, reminder, standard, caution, verification, sterilization, hidden danger, prudence, prevention, health status, warning, safety hazard, precautions, sense of security, harmlessness, standard, compliance, stability

).

The four topics comprehensively characterize user requirements for scalp detectors from different dimensions:

(1)

Topic 1 “Functional Quality” focuses on product performance and reliability, covering core parameters such as resolution, accuracy, and stability to ensure that users’ expectations for detection outcomes are met.

(2)

Topic 2 “Product Experience” concerns the convenience of operational procedures and interface friendliness, including usability, intuitiveness, and after-sales service, which directly shape the overall user experience.

(3)

Topic 3 “Human Factors Engineering Design” delves into ergonomics and industrial design, involving adjustability convenience, tactile comfort, and multi-angle adaptability, balancing visual and haptic experiences.

(4)

Topic 4 “Safety” centers on user health and safety assurance, encompassing risk warnings and compliance measures, which constitute a critical prerequisite for product selection.

The four themes above serve as primary indicators. Based on theme-specific keywords, user requirements are further categorized as shown in

Table 5. User requirement indicators for Scalp detector.

Primary Indicator	Secondary Indicator	Requirement Description	Thematic Keywords	Number
A. Functional Quality	Recognition Accuracy	Ability to detect targets such as hair follicles and dandruff	Precision, identification, error, resolution, detector	A1
	Image Clarity	Clarity and detail representation of microscope/probe imaging	Clear, high-definition, imaging, detail, magnification	A2
	Detection Speed	Timeliness of the detection process and efficiency of result output	Fast, real-time, response, process, minutes	A3
	Result Consistency	Stability of repeated measurements on the same sample	Stable, reliable, repeatability, fluctuation, consistency	A4
B. Product Experience	Operational Ease	Simplified operation workflow and improved interface friendliness	Easy to use, simple, intuitive, friendly, tutorial	B1
	Contact Comfort	Comfort of probe-to-scalp contact	Gentle, imperceptible, soft, contact, pressure	B2
	Learning Resources	Learning materials to help users quickly master operation	Tutorial, video, guidance, instructions, quick start	B3
	Result Visualization	Intuitive presentation of detection results and progress	Prompt, visualization, report, status, progress	B4
C. Human Factors Engineering Design	Handle Grip	Ergonomically comfortable grip design	Grip, fit, anti-slip, fatigue, handle	C1
	Probe Adhesion	Conformity of the probe to the scalp’s curved surface	Curvature, conformity, contact, area, adaptability, angle	C2
	Portable Storage	Portability of the device and ease of storage	Lightweight, compact, foldable, storage, volume	C3
	Scenario Adaptability	Ability to adapt to diverse usage environments	Waterproof, dustproof, thermal drift resistance, drop resistance, shock resistance	C4
D. Safety	Misdiagnosis Risk	Reliability of identifying high-risk lesions	Misdiagnosis, risk, diagnosis, disease, fungus	D1
	Biosafety	Biocompatibility and hygiene assurance of contact components	Non-toxic, low-allergenicity, biocompatible, sterile, material	D2
	Privacy Security	Security protection for user data storage and transmission	Encryption, privacy, storage, transmission, access control	D3
	Mishandling Protection	Protective mechanisms to prevent accidental operations	Protection, locking, warning, insurance, fault tolerance	D4

, constituting the user requirement elements for the scalp detector discussed in this paper.

4.1.2. User Requirement Weight Calculation and Analysis

(1)

First, Algorithm 1 was used to call the Baidu Sentiment Analysis API to obtain sentiment polarity and confidence score results, as illustrated in

Table 6. Example of Sentiment Polarity and Confidence Analysis for User Comments.

Text Content	Emotional Polarity	Probability of Heads	Confidence
I used it to detect the status of hair follicles, and the results seemed quite accurate, similar to what the doctor said.	Positive (2)	0.952	0.894

. Finally, the user preference weights $w_j^{user}$ were calculated through normalization, and the results are shown in Figure 7.

(2)

IVNS-AHP Subjective Weighting

Based on text mining results from user reviews, this paper constructs a hierarchical model of user requirements for scalp detector, as shown in Figure 8.

To scientifically quantify the weighting of requirements at each level and construct an effective pairwise comparison matrix, this paper employs the Delphi Method to gather opinions from five domain experts and tenterminal user. The final results are presented in

Table 7. Criterion-level pairwise comparison matrix.

	A	B	C	D
A	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]	[0.70, 0.80], [0.15, 0.25], [0.20, 0.30]	[0.25, 0.35], [0.70, 0.80], [0.65, 0.75]
B	[0.15, 0.25], [0.80, 0.90], [0.75, 0.85]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.55, 0.65], [0.30, 0.40], [0.35, 0.45]	[0.20, 0.30], [0.75, 0.85], [0.70, 0.80]
C	[0.20, 0.30], [0.75, 0.85], [0.70, 0.80]	[0.35, 0.45], [0.60, 0.70], [0.55, 0.65]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]
D	[0.65, 0.75], [0.20, 0.30], [0.25, 0.35]	[0.70, 0.80], [0.15, 0.25], [0.20, 0.30]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]

,

Table 8. Functional quality A pairwise comparison matrix.

	A1	A2	A3	A4
A1	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]
A2	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
A3	[0.15, 0.25], [0.80, 0.90], [0.75, 0.85]	[0.05, 0.15], [0.95, 1.00], [0.90, 0.95]	[0.50, 0.50], [0.50, 0.50], [0.50,0.50]	[0.25, 0.35], [0.70, 0.80], [0.65, 0.75]
A4	[0.05, 0.15], [0.95, 1.00], [0.90, 0.95]	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]	[0.65, 0.75], [0.20, 0.30], [0.25, 0.35]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]

,

Table 9. Product Experience B Paired Comparison Matrix.

	B1	B2	B3	B4
B1	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
B2	[0.05, 0.15], [0.95, 1.00], [0.90, 0.95]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
B3	[0.00, 0.10], [1.00, 1.00], [0.95, 1.00]	[0.15, 0.25], [0.80, 0.90], [0.75, 0.85]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.25, 0.35], [0.70, 0.80], [0.65, 0.75]
B4	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]	[0.65, 0.75], [0.20, 0.30], [0.25, 0.35]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]

,

Table 10. Human Factors Engineering Design C Pairwise Comparison Matrix.

	C1	C2	C3	C4
C1	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.65, 0.75], [0.20, 0.30], [0.25, 0.35]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]
C2	[0.25, 0.35], [0.70, 0.80], [0.65, 0.75]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.70, 0.80], [0.15, 0.25], [0.20, 0.30]
C3	[0.05, 0.15], [0.95, 1.00], [0.90, 0.95]	[0.00, 0.10], [1.00, 1.00], [0.95, 1.00]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.25, 0.35], [0.70, 0.80], [0.65,0.75]
C4	[0.15, 0.25], [0.80, 0.90], [0.75, 0.85]	[0.20, 0.30], [0.75, 0.85], [0.70, 0.80]	[0.65, 0.75], [0.20, 0.30], [0.25, 0.35]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]

and

Table 11. Security D pairwise comparison matrix.

	D1	D2	D3	D4
D1	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.70, 0.80], [0.15, 0.25], [0.20, 0.30]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]
D2	[0.20, 0.30], [0.75, 0.85], [0.70, 0.80]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]	[0.30, 0.40], [0.65, 0.75], [0.60, 0.70]
D3	[0.00, 0.10], [1.00, 1.00], [0.95, 1.00]	[0.15, 0.25], [0.80, 0.90], [0.75, 0.85]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]	[0.10, 0.20], [0.90, 0.95], [0.80, 0.90]
D4	[0.05, 0.15], [0.95, 1.00], [0.90, 0.95]	[0.60, 0.70], [0.25, 0.35], [0.30, 0.40]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.50, 0.50], [0.50, 0.50], [0.50, 0.50]

. User requirement weights were derived using Equations (12)–(18), with the results shown in

Table 12. User requirement weights.

Criteria Layer	Criteria Layer Weight	Indicator Layer	Indicator Layer Weight	IVNS-AHP Weight	Composite Subjective Weight	Consistency Ratio CR
A	0.2907	A1	0.4255	0.1236	0.0974	0.0673
		A2	0.2746	0.0798	0.0799
		A3	0.1452	0.0422	0.0331
		A4	0.1547	0.0450	0.0335
B	0.194	B1	0.4524	0.0878	0.0727	0.0625
		B2	0.2496	0.0484	0.0677
		B3	0.1221	0.0237	0.0566
		B4	0.1759	0.0341	0.0531
C	0.1557	C1	0.3871	0.0602	0.0728	0.0555
		C2	0.3096	0.0482	0.0678
		C3	0.1002	0.0156	0.0549
		C4	0.2031	0.0316	0.0614
D	0.3596	D1	0.4205	0.1512	0.0751	0.0515
		D2	0.2492	0.0896	0.0638
		D3	0.0972	0.0350	0.0286
		D4	0.2332	0.0838	0.0815

.

4.2. Experimental Design for Scalp

4.2.1. Experimental Environment and Parameter Configuration

This experiment was conducted on the Windows 10 Education operating system using Python 3.11.9, PyTorch 2.1.1, and CUDA 12.1. The hardware configuration is as follows: CPU: Intel^® Core™ i9-9900K (Intel, Santa Clara, CA, USA); Memory: 64 GB DDR4 3200 MHz; Graphics Card: NVIDIA GeForce RTX 3060 (12 GB) (NVIDIA, Santa Clara, CA, USA).

4.2.2. Dataset Construction

This paper constructs a dataset dedicated to scalp inspection. Data acquisition was carried out using a specialized scalp detector jointly deployed with a partner client. The device is equipped with 50× and 200× optical lenses; at 50× magnification it can operate under three standard illumination modes (UV light, polarized light, and white light), enabling the capture of high-resolution scalp images under strictly controlled conditions. To ensure practical applicability, the images used in this paper come from scalp photos collected during the development of a scalp inspection system for the client. All acquisition procedures followed strict privacy protection protocols, and the images were de-identified after collection to ensure that no personally identifiable information is contained.

The original collection comprised 800 scalp images at 1920 × 1080 resolution. After quality screening, 28 blurred or strongly reflective images were removed, leaving 772 images. These were then cropped to 640 × 640 using a segmentation script, yielding a final dataset of 5035 images with 20,863 annotated instances. Annotation was conducted on a self-deployed CVAT platform on Tencent Cloud (see Figure 9). We defined three L0-level categories (singleroot, doubleroot, white-dandruff), with labeling performed by five annotators and reviewed by two experts. Inter-annotator agreement was assessed by randomly sampling 100 images for independent dual annotations at an IoU threshold of 0.5, resulting in an average IoU of 0.87 and a category agreement rate of 92.0%. The dataset was split into a training set with 2999 images and 12,343 instances, a validation set with 1044 images and 4440 instances, and a test set with 992 images and 4080 instances.

4.2.3. Algorithm Selection and Parameter Configuration

During the network training phase, to ensure experimental fairness and result reliability, this paper selected four representative object detection algorithms for comparative analysis. Training parameters were uniformly configured based on actual hardware environments. The algorithm selection and parameter settings are detailed in

Table 13. Evaluation algorithm and training parameters.

Parameter	Algorithm for Evaluation
	Faster R-CNN	SSD-VGG16	YOLOv7	YOLOv8n
Representative Direction	High-Precision Positioning and Classification [43]	Balancing speed and accuracy [44]	Best overall performance [45]	Lightweight and Efficient Design [46]
learning rate	1 × 10−3	1 × 10−3	1 × 10−3	1 × 10−3
batch size	8	8	8	8
weight decay	5 × 10−4	5 × 10−4	5 × 10−4	5 × 10−4
Momentum	0.9	0.9	0.9	0.9
Epochs	300	300	300	300

.

The evaluation algorithm encompasses the following performance metrics: Precision, Recall, mAP@0.5, F1 Score, FPS, and Parameters. The calculation formulas are as follows:

$$Precision={\displaystyle \frac{TP}{TP+FP}}\times 100\%$$

(42)

$$Recall={\displaystyle \frac{TP}{TP+FN}}\times 100\%$$

(43)

$$mAP={\displaystyle \frac{1}{c}}{\displaystyle \sum _{k=0}^{c}A{P}_k}$$

(44)

where TP and FP represent the number of correctly predicted positive cases and incorrectly predicted positive cases, respectively; FN denotes the number of incorrectly predicted negative cases; AP_k is the average detection accuracy for the k-th category; c is the number of target categories.

4.2.4. Experimental Results

The performance comparison results of each algorithm are shown in

Table 14. Experimental result.

Algorithms	mAP@50	Precision	Recall	F1 Score	FPS	Parameters (M)
Faster R-CNN	0.71	0.68	0.89	0.77	9	41
SSD-VGG16	0.87	0.82	0.85	0.83	35	26.8
YOLOv7	0.83	0.79	0.86	0.82	45	37.18
YOLOv8n	0.89	0.89	0.87	0.88	55	3.16

. The detection results of different algorithms on the scalp detection dataset are illustrated in Figure 10.

As shown in Figure 11, four subplots provide a multidimensional comparison of the algorithms in terms of accuracy, efficiency, and model complexity based on their performance on the self-built dataset. In the FPS–mAP@50 plot (a), YOLOv8n appears in the upper-right region, reflecting an excellent balance between detection accuracy and real-time capability. SSD-VGG16 also achieves relatively high precision with moderate speed, while Faster R-CNN remains in the lower-left quadrant due to its limited inference efficiency. In the Params–F1 Score plot (b), YOLOv8n attains the highest F1 score with the smallest parameter count, highlighting its lightweight yet effective architecture. SSD-VGG16 and YOLOv7 show moderate trade-offs between complexity and performance, whereas Faster R-CNN involves higher computational cost with relatively lower comprehensive accuracy. The Recall–Precision plot (c) indicates that SSD-VGG16 and YOLOv8n maintain a desirable equilibrium between detection completeness and correctness, while Faster R-CNN exhibits higher recall but lower precision, implying more false positives. The integrated bubble chart (d) further illustrates the distinct characteristics of each algorithm, with YOLOv8n showing a favorable combination of speed, precision, and overall balance under the experimental conditions. These results reveal the performance tendencies of different models on the customized dataset.

4.3. Final Weighting of Technical Indicators

4.3.1. Objective Weighting of Indicators via the EWM

Based on the experimental results and the calculations in Section 3.2 using Equations (19)–(25) the objective weights for each algorithm metric are determined, with the results presented in

Table 15. Indicator weights under the EWM.

Indicator	Meaning	Indicator Type	Information Entropy	Weight
mAP@50	Core Metric for the Comprehensive Performance of Model Localization and Classification [47]	+ 1	0.7827	0.1305
Precision	Assessing the accuracy of model predictions [48]	+	0.7662	0.1404
Recall	The ability of a model to detect all positive class samples [49]	+	0.6894	0.1865
F1 score	Harmonic Mean of Precision and Recall [50]	+	0.7485	0.1510
FPS	Key metrics for evaluating model inference speed and real-time performance [51]	+	0.7737	0.1359
Parameters (M)	Core metrics for evaluating model size, complexity, and memory consumption [52]	− 2	0.5738	0.2559

¹ “+” indicates a positive indicator, ² “−” indicates a negative indicator.

.

4.3.2. Computation of Subjective–Objective Indicator Mapping

To ensure the scientific rigor and applicability of the mapping matrix, we established the following principles after multiple in-depth consultations with domain experts: indicators that have a direct, linear relationship with technical metrics (e.g., recognition accuracy, detection speed) are directly mapped, with higher values assigned to stronger associations; for composite indicators, we decompose their intrinsic components and include only the parts that can be optimized by algorithms in the mapping, attributing the remaining parts to other R&D processes and marking them as N/A; indicators that depend entirely on hardware conditions, software frontend, or procedural specifications are excluded from algorithm evaluation, with their weights collectively marked as N/A. This approach ensures a clear evaluation scope and well-defined boundaries. The construction results of the mapping matrix are shown in

Table 16. Subjective-objective indicator mapping matrix.

User Requirements	mAP@50	Precision	Recall	F1 Score	FPS	Parameters (M)	Algorithm Weight	Attribute Classification
A1	0.35	0.25	0.20	0.20	— *	—	1.00	Algorithm Core Performance
A2	—	—	—	—	—	—	0.00	Hardware Dependency
A3	—	—	—	—	1.00	—	1.00	Algorithm Efficiency
A4	0.20	0.20	0.30	0.30	—	—	1.00	Algorithm Robustness
B1	—	—	—	—	—	—	0.00	Interaction Design
B2	—	—	—	—	—	—	0.00	Industrial Design
B3	—	—	—	—	—	—	0.00	Product Operations
B4	—	—	—	—	—	—	0.00	Interaction Design
C1	—	—	—	—	—	—	0.00	Industrial Design
C2	—	—	—	—	—	—	0.00	Industrial Design
C3	—	—	—	—	—	0.30	0.30	Hybrid Metrics (Algorithm/Industrial Design)
C4	0.10	0.10	0.10	0.10	—	—	0.40	Hybrid Metrics (Algorithm/Hardware)
D1	0.15	0.40	0.15	0.10	—	—	0.80	Algorithm Reliability
D2	—	—	—	—	—	—	0.00	Materials and Compliance
D3	—	—	—	—	—	—	0.00	Information Security
D4	—	—	—	—	—	—	0.00	System Design

* Indicators marked as Not Applicable (N/A) are uniformly denoted as “—”. Algorithm weights reflect the correlation between user requirement and algorithm performance.

.

4.3.3. Final Weight Calculation

Based on the preceding content and Equations (26) and (27), the final weights of the indicators are calculated as shown in

Table 17. Final weight.

Technical Indicators	Mapping Weight (Wmap)	Weights by the EWM (Wtech)	Wmap × Wtech	Final Weighting (Wfinal)
mAP@50	0.0582	0.1305	0.0076	0.1851
Precision	0.0672	0.1404	0.0094	0.2300
Recall	0.0469	0.1865	0.0087	0.2132
F1 Score	0.0432	0.1510	0.0065	0.1590
FPS	0.0331	0.1359	0.0045	0.1097
Params(M)	0.0165	0.2559	0.0042	0.1029

.

4.4. Algorithmic Comprehensive Ranking

Improved VIKOR Method Calculation

Based on the VIKOR calculation method described in Section 3.5, five domain experts were again invited to score the technical indicators according to Table 2. The comprehensive results are presented in

Table 18. Decision matrix.

Algorithms	mAP@50	Precision	Recall	F1 Score	FPS	Parameters (M)
Faster R-CNN	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.50, 0.60], [0.35, 0.45], [0.40, 0.50]	[0.60, 0.70], [0.25, 0.35], [0.30, 0.40]
SSD-VGG16	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]
YOLOv7	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]	[0.70, 0.80], [0.15, 0.25], [0.20, 0.30]
YOLOv8n	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.75, 0.85], [0.10, 0.20], [0.15, 0.25]

.

According to Equations (29)–(32), the positive and negative ideal solutions are determined, with results shown in

Table 19. Positive and negative ideal solutions.

Indicator	Optimal Solution	Negative Ideal Solution
mAP@50	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
Precision	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]
Recall	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
F1 Score	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]	[0.80, 0.90], [0.05, 0.10], [0.10, 0.20]
FPS	[0.90, 0.95], [0.00, 0.05], [0.05, 0.15]	[0.50, 0.60], [0.35, 0.45], [0.40, 0.50]
Parameters (M)	[0.60, 0.70], [0.25, 0.35], [0.30, 0.40]	[0.95, 1.00], [0.00, 0.00], [0.00, 0.10]

. Based on the improved VIKOR method proposed in this paper and Equations (33)–(41), we compute the group utility, individual regret, and compromise index, and perform comparative ranking; the results are presented in

Table 20. Positive and negative ideal solutions Comprehensive evaluation results of the algorithm.

Algorithms	Improved IVNS-VIKOR Comprehensive Evaluation Results
	Q Value (v = 0.5)	S Value	R Value	Wk 1	ΣP 2	Ranking
Faster R-CNN	1.0000	0.5487	0.1097	0	0.0000	4
SSD-VGG16	0.7045	0.5000	0.1066	1	1.0000	3
YOLOv7	0.1567	0.3010	0.1029	2	2.1809	2
YOLOv8n	0.0000	0.1878	0.1029	3	2.8191	1

¹ W_k denotes the number of pairwise comparisons won. ² ΣP represents the overall advantage score.

.

5. Empirical Research Results Analysis

5.1. Sensitivity Analysis of the Parameter $\alpha$ in the Composite Subjective Weight

To validate the rationality of the parameter α in the composite subjective weight, this section systematically analyzes different values of α (see Figure 12).

The box plot illustrates the distribution of weight differences (ΔW) across the 16 secondary indicators under varying values of α. As α increases from 0.1 to 0.9, the model’s sensitivity to user preferences gradually strengthens. Within the range of α = 0.5–0.7, weight fluctuations are minimized, indicating good stability and robustness. Notably, at α = 0.5, the mean weight difference (ΔW) approaches zero, signifying that the weighting system achieves a balanced state between user preferences and expert judgment. This equilibrium point represents the stage where the decision process equally reflects subjective user orientation and expert analytical rationality.

At α = 0.6, the red box is markedly smaller than those at other α values, with the interquartile range (0.0053), standard deviation (0.0046), and range (0.0192) all reaching their minimums, while the median approaches zero (−0.0002). This indicates that the weight differences are most concentrated, exhibiting minimal fluctuations and the fewest outliers. Overall, the box plot presents a nearly symmetrical distribution centered around α = 0.5, confirming that the weight fusion mechanism maintains both structural balance and robustness. Accordingly, α = 0.6 is selected as the setting closest to this equilibrium point—slightly inclined toward user preferences—thereby aligning with the user-centered evaluation principle while preserving the rigor and stability of expert decision logic.

Furthermore, the ranking outcomes of the four detection algorithms under different values of α (see Figure 13) further validate the robustness of the proposed weighting mechanism. Within the range of α = 0.1–0.6, the ranking pattern remains completely consistent, with YOLOv8n and YOLOv7 continuously occupying the top two positions, followed by SSD-VGG16 and Faster R-CNN. As α increases to 0.7–0.9, only a minor exchange occurs between Faster R-CNN and SSD-VGG16 in the lower ranks, while the leading algorithms remain unchanged. When α reaches 1.0, YOLOv7 slightly surpasses YOLOv8n, reflecting the strengthened influence of expert weights.

This overall consistency across different α values demonstrates that the decision model is insensitive to moderate parameter variations, confirming that the fusion process effectively balances user-oriented and expert-driven perspectives. The stable ranking structure complements the box plot analysis, providing further evidence that α = 0.6 represents the most robust and interpretable configuration, achieving both internal equilibrium and practical decision stability.

5.2. Sensitivity Analysis of Preference Parameter $v$

To examine the robustness of the decision results with respect to the preference parameter settings, a sensitivity analysis was conducted within the VIKOR framework for v∈{0, 0.1, 0.2, …, 1.00}, and the results are shown in Figure 14. The results indicate that the ranking of the models remains generally stable across different values of v, demonstrating good robustness of the decision outcomes.

YOLOv8n consistently exhibits the best overall performance under all v values, with the lowest Q values and overall advantage score ΣP that increases steadily from 2.5316 to 3.0000 as v grows. This trend suggests that the overall superiority of YOLOv8n further strengthens when greater weight is assigned to group utility in the decision process, securing its top-ranked position.

YOLOv7 maintains Q values close to, but slightly higher than, those of YOLOv8n. In some cases (e.g., v = 0), both models share identical Q values, yet YOLOv7 has a slightly lower ΣP (2.4684 vs. 2.5316). This indicates that although the two models have similar compromise levels, YOLOv8n achieves a higher overall advantage, enabling clearer differentiation in the rankings.

SSD-VGG 16 has Q values between those of YOLOv7 and Faster R-CNN, showing a steady increasing trend in both Q and ΣP (from 0.5441 to 0.8649 and from 0.9606 to 0.8066, respectively) as v increases. This reflects a certain degree of sensitivity to the parameter v; however, its overall advantage score remains higher than that of Faster R-CNN, keeping it in third place.

Faster R-CNN, with Q = 1.0000 under all parameter settings, exhibits the greatest deviation from the ideal solution. Meanwhile, its ΣP values are the lowest and show minimal fluctuation, indicating a clear disadvantage in terms of overall advantage.

5.3. Comparison with the Reference Method

This section aims to systematically compare the ranking performance of the proposed IVNS-AHP + EWM-VIKOR model with several representative approaches under the same evaluation dataset and indicator system (see

Table 21. Comparison of comprehensive performance with baseline methods.

Method ID	Methodological Framework	Environment	Weighting Strategy	Source
Proposed	IVNS-AHP + EWM-VIKOR	IVNS	Subjective: User preferences + AHP (expert); Objective: EWM	This work
M1	IVNS-AHP + EWM-VIKOR	IVNS	Subjective: User preferences + AHP (expert); Objective: EWM	This work (Dissolution)
M2	IVNS-TODIM	IVNS	Objective: Similarity measures and information content based on cross-information	[53]
M3	IVNS-MD-TOPSIS	IVNS	Objective: MD	[54]
M4	IVIF-AHP-TOPSIS	IVIF	Subjective: AHP	[55]
M5	IVPFN-AHP-VIKOR	IVPFN	Subjective: PFAHP	[56]
M6	FIS-AHP-VIKOR	FIS	Subjective: FAHP	[57]
M7	IF-CRITIC-RS-VIKOR	IF	Objective: CRITIC; Subjective: RS	[58]
M8	TFN-AHP-TOPSIS-VIKOR	TFN	Subjective: AHP	[59]

Note: TODIM (an acronym in Portuguese of interactive and multiple attribute decision-making), MD (Maximizing Deviation), IVIF (Interval-Valued Intuitionistic Fuzzy), TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), IVPFNs (interval-valued Pythagorean fuzzy numbers), FIS (fuzzy inference system), IF (Intuitionistic fuzzy), CRITIC (CRiteria Importance Through Intercriteria Correlation), RS (Rank Sum), TFN (triangular fuzzy numbers).

). To ensure fairness and scientific validity of the comparison, all methods are implemented within an identical decision-making scenario and evaluated using the same indicator framework and dataset. The only differences lie in the procedures for weight determination, fuzzy information representation, and ranking algorithms.

Considering that the comparative methods are established under different fuzzy theoretical frameworks (such as IVNS, IVIF, IVPFN, TFN, FIS, and IF), this paper adopts a unified linguistic evaluation scale to convert the original data into fuzzy number representations compatible with each fuzzy environment, thereby ensuring semantic consistency of the information expressed across different methods. Moreover, the processes of fuzzy normalization, attribute weight integration, decision matrix construction, and defuzzification all follow uniform computational logic and operational principles, thereby minimizing the interference of non-model factors in the ranking results.

For models adopting a hybrid subjective–objective weighting scheme, the ratio coefficient between the two sources of information was fixed to a unified value to ensure comparability of weight allocation under consistent parameter settings. For methods relying solely on either subjective or objective weighting, normalization procedures were applied to standardize the weight vectors, ensuring scale consistency across all compared approaches.

In the comparative experiments, the proposed PD-VIKOR approach demonstrates superior ranking precision and discrimination capability in evaluating four target detection algorithms. By integrating both the Q value and the overall preference degree (ΣP), the PD-VIKOR method effectively avoids the ranking ambiguity commonly observed in traditional VIKOR models under extreme parameter settings, while enhancing the differentiation between alternatives. In this experiment, YOLOv8n consistently ranks first and Faster R-CNN last across all methods, indicating a stable consensus in the ranking trend of mainstream models when evaluated from multiple dimensions, including user experience, detection accuracy, and computational efficiency (see

Table 22. Comparison results of different methods.

Method ID	Sorting Methods	1-Faster R-CNN	2-SSD-VGG16	3-YOLOv7	4-YOLOv8n	Ranking
Proposed	$\mathrm{PD}-\mathrm{VIKOR}(\Sigma P,v=0.5)$	0.0000	1.0000	2.1809	2.8191	4 ≻ 3 ≻ 2 ≻ 1
M1	$\mathrm{VIKOR}(Q,v=0.5)$	1.0000	0.9880	0.2945	0.0000	4 ≻ 3 ≻ 2 ≻ 1
M2	$\mathrm{TODIM}\left(\vartheta \right(R_i)$)	0.0000	0.6183	0.7812	0.8476	4 ≻ 3 ≻ 2 ≻ 1
M3	$\mathrm{IVNS}-\mathrm{TOPSIS}({\widehat{\Gamma }}_{\delta })$	0.2174	0.6412	0.7689	0.9256	4 ≻ 3 ≻ 2 ≻ 1
M4	$\mathrm{IVIF}-\mathrm{TOPSIS}({\varphi }_j)$	0.3065	0.7248	0.8256	0.8842	4 ≻ 3 ≻ 2 ≻ 1
M5	$\mathrm{FVIKOR}(Q,v=0.5)$	1.0000	0.6957	0.1472	0.0000	4 ≻ 3 ≻ 2 ≻ 1
M6	$\mathrm{FVIKOR}(Q_i,v=0.5)$	1.0000	0.7083	0.1306	0.0000	4 ≻ 3 ≻ 2 ≻ 1
M7	$\mathrm{IF}-\mathrm{VIKOR}(e_i)$	0.9512	0.5784	0.6452	0.1278	4 ≻ 2 ≻ 3 ≻ 1
M8	$\mathrm{FVIKOR}-\mathrm{TOPSIS}(FCR{S}_i)$	0.1216	0.6318	0.7895	0.9683	4 ≻ 3 ≻ 2 ≻ 1

Note: ΣP—comprehensive superiority degree (higher is better); $Q$—VIKOR aggregation index (lower is better); $R_i$—overall dominance degree in TODIM (higher is better); ${\widehat{\Gamma }}_{\delta }$—relative closeness coefficient in IVNS-TOPSIS (higher is better); ${\varphi }_j$—closeness/similarity coefficient in IVIF-TOPSIS (higher is better); $Q_i$—aggregation value in FVIKOR (lower is better); $e_i$—fuzzy distance to the ideal solution (lower is better); $FCR{S}_i$—comprehensive ranking score in FVIKOR-TOPSIS (higher is better).

).

It is noteworthy that in the M1 method with v = 0, the Q values of models 1 and 2 are both equal to zero, resulting in an inability to effectively distinguish between them. This finding highlights the inherent risk of ranking failure in the traditional VIKOR approach when boundary parameters are applied. In contrast, the proposed PD-VIKOR method introduces the comprehensive superiority degree (ΣP) as a supplementary criterion, enabling effective discrimination even when Q values are identical or extremely close. This enhancement not only improves ranking robustness and interpretability but also extends the applicability of VIKOR to uncertain and imprecise decision-making contexts.

Additionally, the M7 method produces an inconsistent ranking order of “4 ≻ 2 ≻ 3 ≻ 1” (see Figure 15), where SSD-VGG16 outranks YOLOv7, which contradicts their respective scores (0.5784 vs. 0.6452) and the results obtained by most other methods. This inconsistency indicates that M7 is sensitive to minor score differences, potentially influenced by the definition of the fuzzy distance measure or the distribution of score intervals, leading to instability in ranking direction. In contrast, the PD-VIKOR approach maintains a consistent ranking structure under the same dataset, demonstrating stronger ranking stability and result reliability.

6. Conclusions and Future Work

This paper extends the AHP-VIKOR fusion method to IVNS, introduces the PD to improve the VIKOR method, and conducts an empirical analysis of mainstream algorithms using mAP@50, Precision, Recall, F1 Score, FPS and Params as evaluation indicators. The main findings are as follows:

First, this paper combines subjective user preferences extracted through NLP and IVNS–AHP with objective weights derived from the EWM, forming a method for determining fusion weights guided by user perception. The weight coefficient α = 0.6 emphasizes the dominant role of user preferences. At the same time, objective weights constrain and modify the evaluation process, enabling the model to achieve an optimal balance between user experience and data consistency.

Second, in the IVNS environment, the proposed PD-VIKOR method maintains consistent rankings under various preference parameters, demonstrating excellent robustness and sensitivity control. In particular, when Q values are close, the overall dominance ΣP can more accurately capture subtle performance differences between models, thereby improving the resolution and credibility of the ranking results.

Finally, ccross-method validation using TODIM, TOPSIS, and their fuzzy extensions (IVNS-TOPSIS, IVIF-TOPSIS, FVIKOR-TOPSIS) reveals strong consistency in ranking performance, with most methods converging on the order “4 ≻ 3 ≻ 2 ≻ 1”. This convergence not only underscores the theoretical soundness of the perception-based evaluation but also provides empirical evidence supporting the effectiveness of the integrated subjective–objective weighting system.

This paper provides practical guidance for algorithm selection and engineering implementation. In decision-making scenarios that integrate multidimensional performance metrics and user perception, the proposed model effectively assists the R&D team in balancing algorithmic accuracy, processing speed, and resource consumption, thereby offering a scientific basis for selecting the optimal algorithm in the practical deployment of scalp detection devices.

Future studies will focus on further improving data reliability, model adaptability, and interdisciplinary applicability. First, to mitigate potential bias and noise in e-commerce user reviews, future work will employ large language models for deeper semantic understanding, sentiment disambiguation, and context-aware filtering, thereby capturing user intent more accurately and reducing the impact of group bias and linguistic ambiguity. Second, as the current IVNS scale and interval settings depend on expert prior knowledge, subsequent research will explore adaptive and self-learning weighting mechanisms to dynamically adjust membership functions and possibility distributions according to evolving data characteristics. Third, longitudinal analyses and temporal evolution models can be introduced to capture the dynamic nature of user preferences and algorithm performance over time, enabling a more comprehensive understanding of the model’s stability and adaptability. Furthermore, expanding the framework to multi-language and cross-cultural datasets will be considered to examine its generalizability and cultural robustness. In addition, future work will consider integrating the proposed methodology into modular Python scripts to facilitate automated implementation and enhance practical scalability. Finally, the proposed perception-driven decision-making framework can be extended to other intelligent product domains to validate its generalizability and strengthen its role as a human-centered decision-support tool in complex engineering environments.