Research on a Refined Decision-Making Method for the Multimodal Fuzzy Design Intent of Complex Products Based on Noncooperative–Cooperative Game Serialization

Abstract

Refined decision-making of the design intent is a key factor affecting the iterative design of complex equipment products. While current research on design intent decision-making generally emphasizes methodological innovation, it often neglects the individualized and fuzzy expressive characteristics of cognitive agents, as well as the actual status of the research object. This oversight leads to uncertainty in both design intent and design outcomes. To address these issues, in this paper, a refined decision-making method for the multimodal fuzzy design intent of complex products based on noncooperative–cooperative game serialization is proposed. First, through scenario analysis, the fuzzy design intent evaluation process of different cognitive agents is transformed into a cooperative game model based on a fuzzy network, achieving a preliminary assessment of design intent. On this basis, a noncooperative game-based refined matching and decision-making model for design intent across different dimensions is constructed, thereby completing the final design intent decision-making for a specific product model. Finally, the proposed method is applied to the design intent decision-making process of a CKA6180 CNC machine tool, yielding the conclusion that the two design intents of “good protective performance” and “grand appearance” should be prioritized, thereby verifying the practicality and effectiveness of the method. The analysis of the results reveals the following: ① The application of scenario analysis theory enables a more comprehensive and precise characterization of the design intents of different cognitive agents; ② The construction of a model combining a fuzzy network with a cooperative game facilitates a more complete representation and evaluation of multimodal fuzzy design intent data; ③ The integration of a refined design concept with a noncooperative game model leads to more definitive design intent decision outcomes, thereby reducing the “disturbance” of experience dependence in the early design phase and consequently enhancing subsequent design satisfaction.

1. Introduction

Product innovation design is a creative activity that achieves effective mapping from design problems to the solution space, constituting a systematic engineering endeavour involving interdisciplinary and cross-domain participation [1]. It primarily encompasses aspects such as requirement identification, conceptual design, scheme iteration, and design decision-making [2]. Specifically, this process typically follows a top-down approach, starting from product design intent and then proceeding to functional design and, finally, to structural design [3]. With advancements in cognitive science and the evolution of design intent, this design process has transformed into a complex one involving multiagent participation and multiple coexisting intents, exhibiting significant multicriteria decision-making attributes [4]. This shift aims to ensure that product design better aligns with human-centric needs, thereby establishing a truly human-centred [5], human–machine collaborative innovation development model [6]. Regarding complex products, their development is inherently characterized by long cycles, stringent quality control, and high maintenance requirements, subjecting the process to numerous risks, including market risk, R&D risk, and manufacturing risk [7]. Concurrently, market and user demands exhibit trends of rapid change, personalization, and diversification. Driven by these dual factors, dynamic and fuzzy uncertainty have become critical attributes permeating the entire design process, particularly during the dynamic evolution of design intent [8]. Therefore, it is necessary to conduct evaluation and decision-making on the multimodal data generated in this process to mitigate product development risks from the source [9].

During the design intent analysis phase, it is essential to identify relevant stakeholders and elucidate on various requirements [10] and to subsequently develop design function architecture and implementation. Often, differences in knowledge backgrounds prevent participants from accurately describing their design intent for a specific product [11]; they tend to propose fuzzy design intents or concepts on the basis of experience with similar products [12]. Moreover, different categories of participants may exhibit different design intents for the same product. Given the diversity in multiagent backgrounds, they may even hold divergent views [13,14]. However, resource constraints dictate that not all design intents can be fulfilled. These intents vary according to specific scenarios and have different priorities. In the context of group multi-attribute decision-making [15,16] research, participants whose consensus level falls below a preset threshold are required to modify their viewpoints. This mandatory adjustment may induce psychological resistance, as individuals are generally reluctant to relinquish their positions easily, thus posing challenges to achieving design intent consensus [17]. An ideal strategy is to identify and prioritize the implementation of high-value intents characterized by high importance and low cost [18]. Consequently, the design team must prioritize design intents on the basis of their importance and relevance to actual product characteristics, with a focus on fulfilling key design intents to achieve a maximal degree of design cognitive symmetry [19]. Existing research on multi-attribute decision-making encompasses various methods and objects. For instance, Zhao et al. [20] combined Kansei Engineering with cloud models and incorporated multi-view evaluation and subjective–objective comprehensive weighting to construct a more refined and reliable multi-attribute decision-making model for product form design schemes. Ahmed et al. [21] integrated the powerful uncertainty-handling capability of type-2 neutrosophic sets with the simplicity and effectiveness of the ARAS method to develop and validate a novel hybrid decision-making approach called N-type-2 ARAS, thereby providing a reliable and robust solution for the complex sustainability decision-making problem of ELV recycling facility location. Xu et al. [22] proposed an intelligent decision-making method based on multi-attribute remaining life scenarios. By analyzing the coupling failure states of physical, technological, and economic life, and by optimizing Bayesian networks using substance-field models and interpretative structural modelling, they achieved rapid and accurate decision-making for the remanufacturing strategies of used electromechanical products. Ibrahim et al. [23] extended the Root Assessment Method (RAM) to the spherical fuzzy environment for the first time and constructed a complete decision-making process of “objective weighting (Entropy Weight Method) + scheme ranking (RAM)” to address the complex real-world problem of selecting power generation technologies.

As can be seen from the above research, although the existing multi-attribute decision-making processes have yielded rich results for different research objects and methods, in the field of product innovation design, the targets are mostly multiagents such as users, designers, and decision-makers. These agents are rich in emotion and simultaneously influenced by factors such as policy, economy, and regional culture. As a result, the expression and outcomes of design intent are typically not deterministic or unique but rather fuzzy and perceptual, characterized by multidimensionality, dynamism, and complexity [24], thereby forming multimodal fuzzy design intents [6]. This necessitates that in the decision-making process of design intent, the environment of the relevant cognitive agents, their personalized expression methods, and the characteristics of the product itself must be fully considered. Relevant methods should be employed to gradually refine and clarify the fuzzy intent information [25], forming a serialized research model with coherent logical relationships [26].

Therefore, in this study, a refined decision-making method for the multimodal fuzzy design intent of complex products based on noncooperative–cooperative game serialization is proposed. In detail, the following Research Questions (RQs) are addressed:

RQ1. 

How can the design intents of different cognitive agents be identified and represented in specific scenarios?

RQ2. 

How can the fuzzy design intents of different cognitive agents be represented and subjected to multi-criteria decision-making for related products?

RQ3. 

How can more refined design intent matching be performed for related products with personalized characteristics?

On this basis, first, scenario analysis theory is applied to perform initial intent recognition for multiple agents (primarily users in usage scenarios and designers in design scenarios) across different situations. Afterwards, on the basis of fuzzy evaluation, complex network theory, and cooperative game theory, a cooperative game model incorporating fuzzy networks is constructed to perform multi-criteria decision-making regarding the importance of each design intent. Finally, on the basis of the relevant functions and features of the specific actual product model, a multidimensional noncooperative game model is constructed to evaluate the degree of match between the design intent and the actual product from different dimensions, thereby completing the final stage of design intent decision-making.

The remainder of this paper is organized as follows. Section 2 reviews related studies (including intent decision-making and the application of game theory in innovation design). Section 3 introduces the theoretical framework and methodological construction of the entire research process. Section 4 presents a case study verification and discusses the research results and implications. Finally, Section 5 provides the conclusions of this study and suggestions for future research.

2. Related Studies

2.1. Design Intent Decision-Making

Design intent evaluation and decision-making are crucial steps in the product innovation design process [27]. Existing studies have approached this process from various perspectives using different methods. For instance, to address design intent change issues in complex product innovation design, Sun et al. [28] constructed a design team and design intent change task model using extension theory, quantified the effect of the generalization of design team experience on execution intent, achieved precise matching between change intent and design teams, improved the efficiency of handling changes in innovation design, and provided a new technical framework for dynamically responding to design intent changes. With respect to product remanufacturing innovation design, one study [29] proposed a knowledge graph-based design intent recognition model that considers the dual dimensions of customer requirements and product failure characteristics and mapped standardized dual-dimensional requirements to design intent nodes in the knowledge graph. The effectiveness of the model was verified using a machine tool remanufacturing design case. Another study [30] constructed a complete technical system for emotional requirements encompassing “extraction–quantification–mapping–optimization”, addressed issues of fuzzy requirements and low correlation with design features in traditional emotional design and provided a reusable technical path for emotion-driven product innovation design. A desk lamp case study verified that the method can accurately match user emotional preferences with product design, filling the gap in quantitative mapping between emotional needs and design features. Yu et al. [31] addressed the difficulty in balancing requirements with enterprise operational constraints in the innovative design of elderly home care service product families and proposed a requirement-driven service product family optimization design method. They applied the Kano model combined with genetic algorithms to elderly care service product family design, constructing a systematic path of “requirement classification–constraint integration–solution optimization”, thereby solving problems of difficult requirement quantification and disconnect from enterprise cost and profit in service product family design. Shie et al. [32] addressing the difficult quantification of emotional needs and disconnect from technical solutions in the innovative design of children’s digital reading book product–service systems (PSS) and proposed an abductive logic-based “4C” design model that integrates Kansei Engineering (KE), the theory of inventive problem solving (TRIZ), and fuzzy techniques. They prioritized core emotional needs using triangular fuzzy numbers and then conducted innovative principle analysis using TRIZ theory to derive design solutions. To address the common issues of single-dimensionality, insufficient generalization capability, and low user participation in existing persona methods, Luo et al. [33] proposed an agent-driven user persona generation method for product design, which includes the stages of data input, persona generation, and application output, thereby expanding the theoretical and technical system of user personas and enabling the more accurate capture of user needs. To address the dynamic changes in customer requirements and the inaccuracy of traditional static requirement models in product innovation design, Walter et al. [34] proposed a dynamic requirement model based on decision field theory (DFT) that incorporates time series factors into requirement forecasting, thus providing cognitive science-based technical support for dynamic requirement modelling. To address the single data source and imbalanced sentiment in online reviews for new energy vehicle user requirements, Yang et al. [35] combined the Kano model to classify 342 extracted attribute words and 10 types of requirements into must-be needs, attractive needs, etc., and performed importance ranking, thereby improving requirement prediction accuracy. With respect to the insufficient linkage between customer requirements and configuration schemes and unsystematic knowledge representation in personalized product configurations, Wu et al. [36] divided requirements into precise requirements (e.g., price and parameters) and fuzzy requirements (e.g., comfort and safety) and combined semantic similarity and matrix matching to increase the accuracy of personalized product configuration schemes. To address the fuzzy uncertainty of customer requirements in the Industrial Intelligent Connection Ecosystem (IICE), Zhang et al. [37] proposed a requirement mining and prediction method based on fuzzy cognitive maps (FCMs) and ARIMA models, analyzed interrequirement relationships and provided a new methodological framework for research that integrates multifeature requirements.

Thus, the expression and decision-making of design intent play significant roles in the product innovation process. However, most existing research focuses on innovations in design evaluation methods and seldom explores the impact of the environment in which the cognitive agents themselves are situated during the early-stage data mining and representation of design intent evaluation, nor does it fully consider the influence of personalized characteristics of the research object. In this study, by constructing a noncooperative–cooperative game serialization method, refined decision-making for the design intent of different cognitive agents in different scenario modes is accomplished, laying the foundation for the subsequent innovation design of corresponding products.

Table 1. Comparison of research outcomes on design intent decision-making in innovation design.

Research Method	Problem Addressed	Author(s) and Reference	Year	Key Advantage
Extension Theory	Design task changes during complex product development.	Sun et al. [28]	2024	Quantifies the universality of design intent through evaluation.
Knowledge Graphs	Existing research only considers customer demands for product performance.	Jiang et al. [29]	2025	Constructs a knowledge graph for design intent identification by combining product failure characteristics with customer requirements.
	Existing research lacks a framework to uniformly represent customer design intent and product information.	Wu et al. [36]	2025	Matches customer requirements with product configuration schemes to achieve decision-making for diverse personalized demands.
BERTopic	Difficulty in predicting user design intent and capturing subtle emotional changes.	Luo et al. [30]	2025	Compensates for the shortcomings of traditional design techniques in capturing user intent and reducing data dimensionality.
Kano Model	Difficulty in directly obtaining accurate user design intent due to limitations in technology and customer group characteristics.	Yu et al. [31]	2024	Performs detailed evaluation and standardized processing of customer requirements to predict potential customer intent.
Design Agent	Existing methods for demand decision-making based on user personas generally suffer from single dimensions, insufficient generalization, and low user participation.	Luo et al. [30]	2025	Proposes an agent-driven method for generating user personas in product design and constructs a generative model, expanding the theoretical and technical system of personas for more accurate demands.
4C Model	Continuous changes in consumer demands for children’s reading products.	Shie et al. [32]	2025	Combines Kansei Engineering, TRIZ theory, and fuzzy techniques to form user design intent at both functional and emotional levels.
Decision Field Theory (DFT)	Inability to capture dynamic changes in design intent during product development and decision-making processes.	Walter et al. [34]	2024	Formulates product strategies through accurate prediction of design intent.
BERT-TCBAD-Kano	Imbalance in review content reduces the accuracy of user intent analysis.	Yang et al. [35]	2024	Improves data prediction accuracy and helps determine the priority of various user intents.
Fuzzy Cognitive Map (FCM) and ARIMA Model	Accurately grasping and predicting customer demands for the Industrial Intelligent Connection Ecosystem (IICE).	Zhang et al. [37]	2025	Effectively realizes the mining and dynamic predictive analysis of implicit customer demands.
Noncooperative– Cooperative Game Serialization	Existing research has not explored the impact of the cognitive agents’ environment on outcomes during the early-stage decision-making of design intent evaluation, nor the correlation between product personalization features and design intent decisions.	This paper	-	Improves the accuracy of design intent identification through scenario analysis of design subjects and consideration of personalized features of the design object.

presents a comparison of research outcomes regarding design intent decision-making in innovation design.

2.2. Game Theory in Product Innovation Design

Game theory [38], also known as the “theory of games”, serves as an important theoretical analysis tool that is primarily used to explain the behavioural patterns of decision-making agents in interactive situations. This theory is based on the fundamental assumption that decision-makers possess complete rationality, meaning that individuals pursue clear external goals and can effectively reason about the actions of other participants. Since the 1950s, game theory has gradually become a focal point in academic research, with its methodological value continuously highlighted. It is now widely applied across multiple disciplines, becoming a key theoretical framework for studying the decision-making behaviours of individuals or groups in contexts of interactive interests. As its core focus is on strategy selection by multiple parties in environments of conflicting interests, game theory is also defined as “a systematic research method for multiperson decision-making problems” [39]. On the basis of differences in decision-making processes and rule structures, game models can be classified along three dimensions: cooperative versus noncooperative games, static versus dynamic games, and complete information versus incomplete information games [40]. With different research backgrounds and problem settings, researchers can select applicable game types for modelling and analysis on the basis of specific objectives.

In product innovation design, several scholars have applied game theory from different perspectives to solve multidecision problems in the design process. For example, Sun et al. [41] combined the rational decision-making advantages of game theory with the user preference analysis capability of perceptual imagery to address issues of reliability in user requirement transformation and coupling in multiobjective design. Lu et al. [42] reported that modular design reuse problems in mechanical and electrical products align well with game theory. Design requirements can be viewed as players, module combinations can be viewed as strategies, and optimal solutions can be derived through game models. Using a stepper machine modular design example, they verified the feasibility of the research process. To address the uncertainty in component reuse strategies and the complexity of intercomponent coupling relationships during the remanufacturing of used mechanical equipment, Chen et al. [38] introduced noncooperative game theory into the remanufacturing reassembly strategy optimization process and established cost-utility functions and lifespan balance functions. Through Nash equilibrium analysis, they identified the optimal strategy combination and completed a study on CA6140 using a lathe remanufacturing strategy. Song et al. [43] combined game theory with TRIZ theory and constructed a product harmful function dynamic identification method through two stages—harm node disadvantage identification and harmful function identification—to provide a decision-making basis for the design stage. Bao et al. [44] addressed the issues of excessively high complexity in both component reuse and assembly for used mechanical and electrical products, which lead to low efficiency, high cost in reupgrading production, and difficulty in responding to mass customization demands, and proposed a noncooperative game-based modular design method for mechanical and electrical products that is oriented towards balancing reuse and assembly complexity, thereby optimizing both production efficiency and cost. They validated the rationality and effectiveness of the method using a fan-bearing seat assembly as an example. Chen et al. [45] combined the fuzzy expression of the house of quality in quality function deployment (QFD) to establish a game theory-based customer requirement determination model that compensates for the inability of traditional customer requirement determination methods to consider multiple stakeholders. To address the fuzziness, randomness, and uncertainty problems in product design scheme evaluation and selection, Li et al. [46] proposed a method for evaluating and selecting design schemes on the basis of cloud models and improved evidence theory. Using game theory concepts, they combined dynamic and static weights of evidence through game combination and improved traditional evidence theory and information fusion on the basis of game combination weights, thus providing a feasible approach for designers to select optimal product design schemes.

On the basis of the above research, game theory can, in multiobjective decision-making processes, determine the optimization scheme most aligned with global expectations by evaluating the degree of contribution of each player to the overall system design. The product innovation design process encompasses multiobjective decision-making problems across multiple stages, constituting a complex system of multiagent, multidecision interactions. The essence of this process lies in coordinating the value orientations, interest demands, knowledge structures, and fuzzy design objectives among different agents, forming cognitive symmetry to achieve balance at the overall system level. At different design stages, corresponding game decision-making forms should be selected on the basis of specific decision-making objectives to ensure the optimality of outputs at each stage, ultimately resulting in a high-quality design scheme. Game theory demonstrates significant theoretical applicability and methodological advantages in decision-making environments characterized by conflict and cooperation. Therefore, this study employs different types of game models to address the corresponding multicriteria decision-making problems at different stages of design intent evaluation.

3. Method

Combining qualitative and quantitative research methods, the research process shown in Figure 1 is constructed and includes multiagent design intent acquisition based on scenario analysis, design intent evaluation based on a cooperative game, and refined design intent decision-making based on a noncooperative game. First, the research object is determined from the product category perspective. Second, the agents that participate in design intent decision-making including users and designers, are identified. Scenario analysis theory is used to identify design intents for both types of agents in different scenarios and obtain initial design intents. Afterwards, by integrating fuzzy thinking with the respective advantages of game theory methods in handling fuzzy multidimensional data interaction and decision-making, a cooperative game model that covers the process from fuzzy data collection and analysis to evaluation is constructed to obtain the initial design intent set. Finally, on the basis of actual product features, a multidimensional noncooperative game design intent matching evaluation model is constructed to complete the final design intent decision-making process.

3.1. Multiagent Design Intent Acquisition Based on Scenario Analysis Theory

With the development of cognitive science, the product innovation design process has evolved into a complex process involving multiagent participation and multiple coexisting intents. Participating agents, primarily users and designers, play important roles. Design intent constitutes the comprehensive requirements put forward by different agents, including users and designers, regarding product performance, structure, form, colour, brand, and other dimensions when they interact with the product in specific usage scenarios, forming the fundamental driving force for product iteration and upgrades, and it exhibits the typical characteristics of high complexity, dynamic evolution, and cognitive ambiguity.

Scenario analysis [47], also known as scenario description or scenario construction, employs assumptions, perception, simulation, and other means to generate a certain scenario and systematically decomposes, associates, and supplements it to obtain the required targets within the scenario. It is an effective tool for analyzing uncertainty. In existing research, Yu et al. [48] proposed a user requirement identification method based on scenario analysis mining negative review data and combined product interaction behaviours to infer problem scenarios during product use, thereby discovering potential user requirements. To help designers acquire valuable innovation opportunities during the fuzzy front end of product development, Liu et al. [49] proposed a scenario-based innovation opportunity identification method for the fuzzy front end, clarified the relationship between scenarios in which products participate and the product innovation process, and discovered product innovation opportunities from the perspective of uncertain future scenario conditions and evolution principles. To address the single path in functional analysis for patent circumvention design and limitations in the circumvention design solution process, Liu et al. [50] proposed a patent circumvention design method based on multilayer functional cognition and scenario analysis. According to differences in multilayer functional forms and the system scope covered by functions, combined with product scenario design concepts, patent circumvention design is performed. To reduce the incidence of maritime accidents caused by fatigue, Pan et al. [51] screened and classified 15 fatigue factors into four categories (environmental, work, sleep, and circadian rhythm), evaluated them through scenario analysis, and established typical scenarios to construct relationships between various elements and fatigue.

The above research confirms that using scenario analysis and setting specific scenarios for different cognitive agents from the perspective of empathy and scenario fusion can result in the construction of an interoperable, fine-grained data layer connecting various agents. Therefore, this study adopts scenario analysis to systematically gather the in-depth cognition of different cognitive agents regarding the research object and to parse their scenario analysis results, thereby acquiring the corresponding design intents. The specific steps are as follows:

3.1.1. User Design Intent Acquisition Based on Product Usage Scenarios

As direct users and service objects of products, users are crucial perception and experience agents throughout the product lifecycle. In the context of increasingly diversified and personalized user demands [52], comprehensively and accurately acquiring user design intent is the key foundation for user-centred product innovation. The process of acquiring user design intent based on usage scenarios encompasses three main core steps: product usage scenario construction, formal expression of design intent based on user usage scenarios, and systematic analysis and comprehensive evaluation of user design intents.

• Product Usage Scenario Construction

The essence of product design is a user-centred innovation process. As users interact with the product over time, a dynamic spatiotemporal relationship gradually forms between the user and the complex product. By analyzing the specific interactive behaviours within this relationship, the behavioural intent at different usage stages can be further identified. The product usage scenario based on users is shown in Figure 2.

2.

Formal Expression of Design Intent Based on User Usage Scenarios

To ensure more intuitive and comprehensive results, a formal expression is used to define the collected initial user design intents.

$$S{C}_{User}=(cu{s}_U^{id},descriptio{n}_U^{int},extrac{t}_U^{int})$$

(1)

Here, $cu{s}_U^{id}$ denotes the serial number of the user design intent, $descriptio{n}_U^{int}$ represents the specific description of the design intent, and $extrac{t}_U^{int}$ denotes the extraction and derivation of the intent.

3.

Systematic Analysis and Comprehensive Evaluation of User Design Intents.

Owing to differences in users’ knowledge backgrounds, their describing methods for scenarios often vary, which can easily lead to cognitive differences and semantic ambiguity in design intent information, thereby reducing the efficiency of experimenters’ understanding and processing. Therefore, this study introduces an expert panel to perform multidimensional processing on initial design intents, including standardized operations such as deletion, merging, and contradictory decision-making, ultimately forming an accurate and usable initial user design intent set: $R_u=\left\{r_{u1},r_{u2},\cdots ,r_{un}\right\}$.

3.1.2. Designer Design Intent Acquisition Based on Product Design Scenarios

As the core agents for solving design problems, designers are key executors driving the innovative design of complex products. By constructing and analyzing design scenarios, one can gain deep insight into designer’s cognitive processes and propose corresponding design intents. These intents, when integrated with those arising from user usage scenarios, not only expand the dimensions of design consideration but also provide more diversified pathways for product iteration. The main steps for acquiring design intent based on design scenarios include design scenario construction, design intent collection, and entropy-based design intent evaluation.

• Designer Design Scenario Construction

Design scenario construction is a critical phase for designers to carry out design activities, providing the fundamental conceptual framework for generating design outcomes. Research indicates that even in the absence of explicit user requirements, designers can proactively drive the innovation process by actively constructing design scenarios. This process is typically built upon the analysis of existing market products and design experience and is comprehensively constructed by integrating current design and manufacturing trends. The specific process is shown in Figure 3.

2.

Designer Design Intent Evaluation Based on Entropy.

Since designers can pinpoint and articulate their design intent regarding the target object with relative precision based on design experience and methodologies, a formal expression of this content is unnecessary. However, the design intents proposed by different designers often exhibit similarity and redundancy. Therefore, in this study an entropy evaluation model for design intent based on entropy theory [53] is constructed and used for related analysis and importance ranking of design intent. The specific steps are as follows:

• The evaluation value of design intent characterized by entropy is as follows:

$$a_j=-\mathrm{k}{\displaystyle \sum _{i=1}^I{P}_{ij}\ln P_{ij}},$$

(2)

where $a_j$ represents the entropy value of the designer’s relevant design intent; i denotes the designer research sample set, $i=1,2,\cdots ,I$; j denotes the initial intent set, $j=1,2,\cdots ,J$; $P_{ij}$ represents the probability of the j-th design intent for the i-th sample, $0\le P_{ij}\le 1$; k denotes a constant, and $k=1/\ln I$.

• Assume that the matrix X of evaluation by designers for the research samples is as follows:

$$X=\left[\begin{array}{cccc}{X}_{11}& X_{12}& \cdots & X_{1J}\\ X_{21}& X_{22}& \cdots & X_{2J}\\ ⋮& ⋮& X_{ij}& ⋮\\ X_{I1}& X_{I2}& \cdots & X_{IJ}\end{array}\right],$$

(3)

where $X_{ij}$ represents the evaluation value of the j-th design intent for the i-th product research sample.

• To reduce errors in the evaluation process by designers, matrix X is normalized to obtain the intent decision matrix $\tilde{X}$, and then the probability $P_{ij}$ of the design intent is obtained, namely,

$$P_{ij}={\tilde{X}}_{ij}/{\displaystyle \sum _{i=1}^I{\tilde{X}}_{ij}},$$

(4)

where ${\tilde{X}}_{ij}$ represents the normalized data of the j-th intent for the i-th sample.

• Applying Formula (2) to calculate the probability $P_{ij}$ of each design intent yields the entropy value $a_j$ for the j-th design intent. The weight of this design intent in the entire evaluation process is $E_j$:

$$E_j={\displaystyle \frac{1-a_j}{{\displaystyle \sum _{j=1}^J(1-a_j)}}},$$

(5)

Sorting on the basis of the weight values of each design intent yields the designer’s initial design intent $R_d=(r_{d1},r_{d2},\cdots ,r_{dm})$.

Based on the above results, initial design intents encompassing user and designer cognition can be formed.

3.2. Design Intent Evaluation Based on a Fuzzy Network Cooperative Game

After obtaining the initial design intents of users and designers, it is necessary to extract comprehensive information that represents both types of cognitive agents. Existing studies typically obtain the correlations among relevant intents through evaluation. However, owing to the inherent uncertainty of evaluation information and its susceptibility to loss during transmission, evaluators usually find it difficult to provide precise numerical values for these relationships, making interval-based expression more suitable. For this purpose, based on fuzzy theory, this study employs interval fuzzy numbers to represent these relationships and establishes a fuzzy complex network [54] with design intents as nodes and interintent correlations as edges. Building upon this foundation, combined with network relationships and attributes, and leveraging the advantage of game theory in handling relationships among multidimensional data, a cooperative game model is constructed to determine the degree of importance of each design intent.

3.2.1. Fuzzy Network Construction

On the basis of the acquired intent information, a questionnaire evaluating the correlation relationships among intents is constructed to obtain the correlation between each intent, defined as a fuzzy number ξ. To ensure evaluation rationality, this study makes the following assumptions [55]:

• The correlation relationships between intent terms reasonably exist;
• The mutual influence relationships between intent terms are symmetric;
• The evaluation relationships provided by the participants are reasonable.

If $\xi =⌈\overline{\xi },\underset{\_}{\xi }⌉$, where $\overline{\xi }$ and $\underset{\_}{\xi }$ are the upper and lower limits of fuzzy number $\xi$, respectively, then

$$\xi =\left\{\begin{array}{c}{\xi }_1=\left[0,0.3\right), \mathrm{Weak} \mathrm{correlation}\\ {\xi }_2=\left[0.3,0.6\right), \mathrm{General} \mathrm{correlation}\\ {\xi }_2=\left[0.6,1.0\right], \mathrm{Strong} \mathrm{correlation}\end{array}\right..$$

(6)

Thus, an intent fuzzy relationship network, as shown in Figure 4, can be constructed.

3.2.2. Study of Fuzzy Network Attributes

• Whitening of Fuzzy Numbers

On the basis of the evaluation results of fuzzy numbers, the correlation among intents can be preliminarily obtained. In actual research processes, specific numerical relationships must be clarified. Therefore, the fuzzy number $\xi$ must be whitened to obtain the whitenized number $\overline{\xi }$:

$$\widehat{\xi }=\sigma \underset{\_}{\xi }+(1-\sigma )\overline{\xi },$$

(7)

where $\sigma$ represents the positional coefficient of fuzzy number $\xi$ and $\sigma =\left[0,1\right]$.

When $0\le \sigma <0.5$, it indicates that the evaluator maintains a positive attitude toward the evaluation object; when $0.5<\sigma \le 1$, it indicates a negative attitude; and when $\sigma =0.5$, it indicates a neutral attitude. Since the evaluators only provide a fuzzy evaluation range, which constitutes objective cognition without reflecting emotional bias, $\sigma$ is set to 0.5 [56], i.e., employing the “neutral attitude” or the mean whitening method for the defuzzification of the fuzzy numbers [57].

2.

Evaluation of Intent Node Attributes in the Fuzzy Network.

In the fuzzy complex network, design intents are treated as nodes, and the correlations between intents are represented as edges. In complex network analysis, the network attributes of nodes are often used as the basis for measuring their importance. Therefore, this study analyses three types of network attributes of design intent nodes—degree centrality [58], betweenness centrality [59], and closeness centrality [60]—and builds a cooperative game model on this basis to comprehensively evaluate the importance of design intent.

In an undirected network, $D=\left\{d_1,d_2,\cdots ,d_K\right\}$ represents the set of all nodes; then, each node attribute [61] is as follows:

• Node Degree Centrality

The degree of a node (degree) refers to the number of edges directly connected to a specific node. In undirected networks, a larger degree value indicates that more nodes are directly connected to that node, suggesting that the node is more important within the network.

Define that $degree(d_t)$ represents the number of nodes directly connected to key node $d_t$, then $degree(d_t)$ is the degree of node $d_t$. If $degree(d_t)\le K-1$ in an undirected network with K nodes, then the degree centrality of node $d_t$ is $C_{\alpha }(d_t)$:

$$C_{\alpha }(d_t)=degree(d_t)/(K-1).$$

(8)

In the evaluation of product design intent networks, the greater the node degree value of an intent term is, the greater its correlation with other intents and the greater its importance.

• Betweenness Centrality

Betweenness centrality is used to quantify the importance of a node acting as a connecting hub within the network. Specifically, it measures its intermediary role by calculating the proportion of shortest paths in the network that pass through a node. A higher betweenness centrality value for a node indicates that a stronger key intermediary function is assumed in information flow or resource dissemination and has a greater impact on the overall connectivity and efficiency of the network. The betweenness of node $d_t$ is $C_{\beta }(d_t)$:

$$C_{\beta }(d_t)={\displaystyle \sum _{a\ne t\ne b}\frac{e_{ab}(d_t)}{f_{ab}}},$$

(9)

where $e_{ab}(d_t)$ denotes the number of shortest paths between nodes $d_a$ and $d_b$ that pass through node $d_t$ and $f_{ab}$ denotes the total number of shortest paths between nodes $d_a$ and $d_b$. Thus, for node $d_t$, the normalized betweenness centrality value is as follows:

$$C_{\overrightarrow{\beta }}(d_t)={\displaystyle \frac{2C_{\beta }(d_t)}{(K-1)(K-2)}}.$$

(10)

The greater the betweenness centrality value of a design intent node is, the stronger its influence on other intents within the network and, consequently, the greater the importance of that design intent.

• Closeness Centrality.

Closeness centrality measures the extent to which a node can influence other nodes through the network. A larger value indicates greater closeness of the node, meaning that the node is closer to the centre of the network, thus indicating that the node is more important.

Define that $l_{ta}$ represents the shortest distance from node $d_t$ to $d_a$. If the sum of the shortest distances from any node to other nodes is ${\displaystyle {\sum }_{a=1}^K{l}_{ta}}\ge K-1$ in a network with K nodes, then the normalized closeness centrality of the node is $C_{\theta }(d_t)$:

$$C_{\theta }(d_t)=(K-1)/{\displaystyle \sum _{a=1}^K{l}_{at}}.$$

(11)

Closeness centrality indicates the position of the node within the network; a larger value indicates a larger weight value for that design intent.

3.2.3. Multiagent Design Intent Importance Evaluation Based on Cooperative Games

In the evaluation of node attributes within fuzzy networks, a single attribute indicator often fails to comprehensively reflect the node’s overall importance. To ensure the objectivity and accuracy of design intent evaluation, this study leverages the advantage of cooperative game models in coordinating multiparty decisions to construct a multiagent design intent evaluation model based on cooperative game theory, which is used to rank the importance of design intent. In this model, the node’s degree centrality, betweenness centrality, and closeness centrality serve as the players in the game. The final game equilibrium yields a weight vector representing the importance of each design intent. The specific steps are as follows:

• We assign weights to the evaluation results of node degree centrality, betweenness centrality, and closeness centrality, to obtain the basic weight vector ${\eta }_w=\left\{{\eta }_{1w},{\eta }_{2w},{\eta }_{3w}\right\} w=(1,2,\cdots ,W)$. Any combination of W different vectors is represented as follows:

  $$\eta ={\displaystyle \sum _{w=1}^W{\sigma }_w{\eta }_w^{\mathrm{T}}},$$

  (12)

  where $\eta >0$, ${\displaystyle \sum _{w=1}^W{\eta }_w^{\mathrm{T}}}=1$, $\eta$ is the comprehensive weight vector, and ${\sigma }_w$ is linear combination coefficient.
• Based on cooperative game theory, the W linear combination coefficients ${\sigma }_w$ are optimized to minimize the deviation between $\eta$ and each ${\eta }_w$; then,

  $$\min {‖{\displaystyle \sum _{w=1}^W{\sigma }_w{\eta }_w^{\mathrm{T}}}-{\eta }_{\delta }^{\mathrm{T}}‖}_2 (\delta =1,2,\cdots ,W).$$

  (13)

  According to the differential properties of the matrices, Formula (13) can be transformed as follows:

  $${\displaystyle \sum _{w=1}^W{\sigma }_w{\eta }_w^{\mathrm{T}}{\eta }_{\delta }^{\mathrm{T}}}={\eta }_w^{\mathrm{T}}{\eta }_{\delta }^{\mathrm{T}}.$$

  (14)

  Transforming it into a linear formula yields the following:

  $$\left[\begin{array}{cccc}{\eta }_1{\eta }_1^{\mathrm{T}}& {\eta }_1{\eta }_2^{\mathrm{T}}& \cdots & {\eta }_1{\eta }_W^{\mathrm{T}}\\ {\eta }_2{\eta }_1^{\mathrm{T}}& {\eta }_2{\eta }_2^{\mathrm{T}}& & {\eta }_2{\eta }_W^{\mathrm{T}}\\ ⋮& ⋮& \ddots & ⋮\\ {\eta }_W{\eta }_1^{\mathrm{T}}& {\eta }_W{\eta }_2^{\mathrm{T}}& \cdots & {\eta }_W{\eta }_W^{\mathrm{T}}\end{array}\right]\left[\begin{array}{c}{\sigma }_1\\ {\sigma }_2\\ ⋮\\ {\sigma }_W\end{array}\right]=\left[\begin{array}{c}{\eta }_1{\eta }_1^{\mathrm{T}}\\ {\eta }_2{\eta }_2^{\mathrm{T}}\\ ⋮\\ {\eta }_W{\eta }_W^{\mathrm{T}}\end{array}\right].$$

  (15)
• By applying Formula (15), $({\sigma }_1,{\sigma }_2,\cdots ,{\sigma }_W)$ can be calculated. After normalization, we obtain the following:

  $${\sigma }_w^{\ast }={\sigma }_w/{\displaystyle \sum _{w=1}^W{\sigma }_w}.$$

  (16)

  Thus, after comprehensive evaluation, the weight vector for the network node’s degree centrality, betweenness centrality, and closeness centrality is obtained as follows:

  $${\eta }^{\ast }={\displaystyle \sum _{w=1}^W{\sigma }_w^{\ast }{\eta }_w^{\mathrm{T}}}.$$

  (17)

  On the basis of ${\eta }^{\ast }$, the comprehensive evaluation value for the t-th design intent is obtained as follows:

  $$G_t={\eta }_{C_{\alpha }(d_t)}^{\ast }{C}_{\alpha }(d_t)+{\eta }_{C_{\overline{\beta }}(d_t)}^{\ast }{C}_{\overline{\beta }}(d_t)+{\eta }_{C_{\theta }(d_t)}^{\ast }{C}_{\theta }(d_t).$$

  (18)

  Consequently, the comprehensive degree of importance of each design intent can be obtained.

The ranking of importance of design intent determines its priority in product design. By setting an importance threshold, design intents exceeding this value can be filtered to form a design intent set $R=\left\{R_1,R_2,\cdots ,R_{rd}\right\}$, thereby providing a basis for subsequent design intent matching and decision-making.

The degree of importance of each design intent determines its priority in product design.

By setting a threshold for the degree of importance, design intents exceeding the threshold are selected to form the design intent set $R=\left\{R_1,R_2,\cdots ,R_{rd}\right\}$, laying the foundation for subsequent design intent matching decisions.

3.3. Refined Design Intent Decision-Making Based on Noncooperative Game

The mining and evaluation of design intent often target only similar products. However, in actual product design processes, design directions and details vary significantly depending on factors such as the brand and model. Therefore, refined [62] design intent decision-making must be performed on the basis of the specific model and characteristics of the research object to ensure that the design direction is more scientific and feasible. As multi-intent decision-making is a discrete optimization process, each element in the design intent set “expects” to be selected to determine the product design direction, constituting a noncooperative game process that can be transformed into a corresponding game problem. Thus, a noncooperative game design intent decision-making model is constructed to complete the refined matching of design intents, laying the foundation for subsequent solution design.

3.3.1. Construction of Noncooperative Game-Related Matrices

Design intent correlation evaluation indicators are determined on the basis of the actual characteristics and evolution trends of the target product. An expert panel then evaluates the correlation of each initial design intent according to the multilevel evaluation criteria shown in Figure 5. On this basis, a design intent correlation evaluation matrix [63], as shown in

Table 2. Design intent and evaluation criteria correlation matrix.

Design Intent Terms	Correlation Indicator|Average Correlation
R1	$C{M}_1^1\left|C{V}_1^1\right.$	$C{M}_2^1\left|C{V}_2^1\right.$	…	$C{M}_{\widehat{m}}^1\left|C{V}_{\widehat{m}}^1\right.$
R2	$C{M}_1^2\left|C{V}_1^2\right.$	$C{M}_2^2\left|C{V}_2^2\right.$	…	$C{M}_{\widehat{m}}^2\left|C{V}_{\widehat{m}}^2\right.$
…	…
Rrd	$C{M}_1^{\dot{r}}\left|C{V}_1^{\dot{r}}\right.$	$C{M}_2^{\dot{r}}\left|C{V}_2^{\dot{r}}\right.$	…	$C{M}_{\widehat{m}}^{\dot{r}}\left|C{V}_{\widehat{m}}^{\dot{r}}\right.$

, is constructed. Here, a higher evaluation score indicates that the design intent is more prominent in the corresponding indicator; i.e., it has a higher degree of matching with the target requirements.

3.3.2. Construction of and Solution to the Noncooperative Game Model

The game process revolves around evaluating targets for outcome decision-making. The evaluation criteria are the players, each intent in the design intent set is a strategy, and the utility values are derived on the basis of the correlation matrix. From Table 1, the degree of satisfaction S of each player for each design intent can be obtained as follows:

$$S(C{M}_{\tilde{m}}^{\tilde{r}})=C{V}_{\tilde{m}}^{\tilde{r}}/(H-1),$$

(19)

where $C{V}_{\tilde{m}}^{\tilde{r}}$ represents the correlation value between the $\tilde{r}$-th design intent and the $\tilde{m}$-th evaluation criterion and can be obtained from Table 1; H represents the maximum number of evaluation criteria.

In the decision-making game for design intent, the utility of each player depends not only on its own strategy choice but also on the strategies of other players—including positively correlated players that promote it and negatively correlated players that inhibit it. The final decision outcome is a comprehensive reflection of the interaction and mutual influence of all the players. On this basis, the following player utility function [42] can be established:

$$\begin{array}{r}U(C{M}_{\tilde{m}}^{\tilde{r}})=S(C{V}_{\tilde{m}}^{\tilde{r}})+\left[{\displaystyle \sum _{m^{+}=1,m^{+}\ne \tilde{m}}^{{\widehat{m}}^{+}}\frac{S(C{V}_{\tilde{m}}^{\tilde{r}})\ast \ln (S(C{V}_{\tilde{m}}^{\tilde{r}}))+S(C{V}_{m^{+}}^{\tilde{r}})\ast \ln (S(C{V}_{m^{+}}^{\tilde{r}}))}{-\ln (\widehat{m})}}\right]\\ -\left[{\displaystyle \sum _{m^{-}=1,m^{-}\ne \tilde{m}}^{{\widehat{m}}^{-}}\frac{S(C{V}_{\tilde{m}}^{\tilde{r}})\ast \ln (S(C{V}_{\tilde{m}}^{\tilde{r}}))+S(C{V}_{m^{-}}^{\tilde{r}})\ast \ln (S(C{V}_{m^{-}}^{\tilde{r}}))}{-\ln (\widehat{m})}}\right]\end{array},$$

(20)

where ${\widehat{m}}^{+}$ and ${\widehat{m}}^{-}$ represent the number of players with positive and negative correlations with the player, respectively, and ${\widehat{m}}^{+}+{\widehat{m}}^{-}=\widehat{m}-1$.

In the noncooperative game process, attention should first be given to maximizing the self-benefit of each player, ensuring that there is no bias towards any criterion in later decision-making. On the basis of Formula (20), a utility matrix can be constructed. Thus, the game utility value for the $\tilde{r}$-th design intent is as follows:

$$u(\tilde{r})={\displaystyle \prod _{\tilde{m}=1}^{\widehat{m}}U(C{M}_{\tilde{m}}^{\tilde{r}})}.$$

(21)

The game utility values are sorted in descending order, and design intents exceeding a predetermined threshold are selected as the final design direction.

4. Case Verification

As the “workhorse” of high-end manufacturing, CNC machine tools play a vital role in the fabrication of key components for major engineering projects [64]. Therefore, on the basis of market research and industrial development conditions, this study verifies the feasibility of the proposed process through the refined decision-making of design intent for a CKA6180 CNC machine tool product from a certain enterprise, which is in urgent need of design improvement. To illustrate the research problem more clearly, the research object is deconstructed from the perspectives of form and functional modules [65]. The original product and its deconstructed view are shown in Figure 6, specifically including components such as the protective cover, observation window, spindle box, and operation panel. This method is also applicable to other product studies.

4.1. User Design Intent Analysis Based on CNC Machine Tool Usage Scenarios

First, from the perspective of CNC machine tool design, relevant users are identified. Through communication, users are determined to include enterprise operators and purchasers of the product. Combining the user usage scenario construction process, through interviews and actual operations with some users, usage scenario analysis and extraction are performed, followed by structured expression and presentation, and some user design intents are obtained, as shown in

Table 3. CNC machine tool user requirements.

No.	Design Intent Description	Design Intent Extraction
1	Machining accuracy meets requirements	High machining accuracy
2	Hope machining is faster than similar products	High machining speed
3	Operating system should be high-end, simple, and easy to operate	Superior operating system
4	Internal machine lighting should be good, clear visibility	Good lighting effect
5	While meeting performance, product should be light weight	Light weight
6	Machining chip fluid separation effect should be good	Easy chip fluid separation
7	Machine should have high power	High power
8	Machine waterproof performance should be good	Good waterproof effect
9	Operation interface layout should be reasonable and easy to operate	Reasonable layout
10	Machine interior should be easy to clean	Easy to clean
11	Buttons should vary in size based on function to prevent errors	Superior ergonomic performance
…	…	…
57	Height of machine control area should be reasonable	Good operational ergonomics

.

An expert panel processes the extracted user design intents from multiple perspectives in conjunction with the actual product characteristics, including deletion and merging, ultimately obtaining the user design intent set on the basis of usage scenarios as follows: Ru = {high machining accuracy, high machining speed, high-end operating system, good lighting effect, easy chip fluid separation, good waterproof effect, reasonable layout, superior ergonomic performance, strong brand identity, good protective performance, easy transportation, clear warning signs, high integrity, good heat dissipation performance, easy disassembly and maintenance, esthetic design, clear visibility}.

4.2. Designer Design Intent Analysis Based on CNC Machine Tool Design Scenarios

On the basis of the design scenario shown in Figure 3, designers typically conduct comparative analyses of similar products before undertaking product innovation to grasp current design trends and form development ideas suitable for their product. Such analysis, excluding identical functionalities, focuses primarily on the design features of the product’s external form.

In this study, the web crawler technology was employed to collect CNC machine tool product images from public sources, including official websites of domestic and international enterprises such as DMG MORI, MAZAK, Haas, Jier, and online images, and an initial sample set containing more than 1500 images was constructed.

Subsequently, using cognitive experiment methods, initial samples were merged and deleted from dimensions such as product type, function, structural layout, and image quality. Professional designers with more than 3 years of experience, according to the KJ method and expert discussion, conducted secondary screening of samples according to the process shown in Figure 7, ultimately selecting 15 representative samples to form the representative sample library shown in Figure 8.

Through in-depth analysis of CNC machine tool products and combining professional design experience and research methods, in this study, perceptual imagery terms and phrases used to describe machine tool product characteristics were collected from multiple channels, such as online product evaluations and product brochures, with 108 relevant expressions initially obtained. On this basis, further interviews and surveys were conducted with graduate students in industrial design, expert panel members, and typical users. After screening and organization, 77 initial representative design intent terms were ultimately obtained, as shown in

Table 4. CNC machine tool design intent vocabulary list.

Interactive	Modern	Precise	Novel	Grand	Convenient	Dull	Warm
Functional	Sturdy	Technological	Sharp	Smooth	Proportionate	Safe	Elegant
…	…	…	…	…	…	…	…
Reliable	Dazzling	Neat	Flat	Esthetic	Rough	Gorgeous	Powerful
Cold	Soft	Fresh	Loose	Rigid

.

To ensure comprehensive coverage of design intent and effectively reduce dimensionality, the correlations among intent terms must be analyzed systematically. For this purpose, values of similarity between terms are first obtained on the basis of a semantic similarity calculation, and then a cluster analysis is performed on the similarity results. In product design research, the number of clusters must typically be greater than 3. To determine a more objective number of clusters, in this study, the clustering results for 3 to 35 classes were systematically analyzed and the corresponding sum of squared errors (SSE) for each category was calculated using Formula (22).

$$SSE={\displaystyle \sum _{\widehat{i}}^{\widehat{k}}{\displaystyle {\sum }_{\widehat{j}\in C_{\widehat{i}}}}}{\left|\widehat{j}-m_{\widehat{i}}\right|}^2,$$

(22)

where $\widehat{k}$ represents the total number of clusters, $m_{\widehat{i}}$ represents the cluster centre of the $\widehat{i}‐\mathrm{th}$ cluster, and $\widehat{j}$ represents the members of the $\widehat{i}‐\mathrm{th}$ cluster.

Error bars are used to represent the changes in the SSE values (as shown in Figure 9). On the basis of the results, when the number of clusters is 7, a better clustering effect can be achieved.

On the basis of the clustering results, seven representative design intent terms are selected: complex, branded, neat, technological, concise, grand, and precise.

To ensure accurate and reliable evaluation data, a Likert scale is used to construct the evaluation process for the correlation between research samples and representative design intent terms, as shown in Figure 10.

Thirty-two subjects participated in this requirement survey, including expert panel members, mechanical design professionals, and graduate students with experience in machine tool form design. The survey results were processed using the mean method, with specific data shown in

Table 5. Evaluation results of the representative sample design intents.

	Complex	Branded	Neat	Technological	Concise	Grand	Precise
Sa1	4.06	3.53	4.38	4.28	3.97	4.22	3.63
Sa2	3.25	3.00	2.84	3.38	3.63	3.22	3.28
Sa3	3.47	2.94	3.09	3.56	3.31	3.03	3.06
…
Sa14	3.75	3.47	3.56	3.78	3.94	3.72	3.59
Sa15	3.63	3.13	3.53	3.50	3.63	3.28	3.50

.

Substituting the data from Table 4 into the requirement entropy Formulas (2)–(5), the weight results for each design intent are calculated as shown in Figure 11. Among them, “grand” has the highest weight at 0.1649, followed by “branded” at 0.1631, whereas “neat” has the lowest weight at 0.1120. In accordance with the actual research situation, the top four ranked terms are selected as the designer’s design intent results on the basis of the design scenario.

Thus, the designer’s initial design intent is obtained as R_d = {grand, branded, technological, precise}.

4.3. Integration and Consolidation of CNC Machine Tool Design Intents Merging Users and Designers

To systematically advance the product design process from inside out, user and designer design intents must be integrated collaboratively. By progressively resolving the fuzziness, redundancy, and conflict among intents, a systematic refinement of the two types of design intents is achieved, thereby yielding the comprehensive design intent:

$$R_{initial}=\left\{\begin{array}{lll}{R}_{initial}^1(\mathrm{fast} \mathrm{processing} \mathrm{speed})\hfill & R_{initial}^2(\mathrm{high} \mathrm{processing} \mathrm{accuracy})\hfill & R_{initial}^3(\mathrm{high}‐\mathrm{end} \mathrm{operating} \mathrm{system})\hfill \\ R_{initial}^4(\mathrm{excellent}‐\mathrm{lighting} \mathrm{effect})\hfill & R_{initial}^5(\mathrm{clear} \mathrm{vision})\hfill & R_{initial}^6(\mathrm{easy} \mathrm{disassembly} \mathrm{maintenance})\hfill \\ R_{initial}^7(\mathrm{outstanding} \mathrm{appearance})\hfill & R_{initial}^8(\mathrm{excellent} \mathrm{man}‐\mathrm{machine} \mathrm{performance})\hfill & R_{initial}^9(\mathrm{strong} \mathrm{brand} \mathrm{type})\hfill \\ R_{initial}^{10}(\mathrm{good} \mathrm{protection})\hfill & R_{initial}^{11}(\mathrm{easy} \mathrm{to} \mathrm{transport})\hfill & R_{initial}^{12}(\mathrm{strong} \mathrm{integrity})\hfill \\ R_{initial}^{13}(\mathrm{warning} \mathrm{obviously})\hfill & R_{initial}^{14}(\mathrm{high}‐\mathrm{tech} \mathrm{feel})\hfill & R_{initial}^{15}(\mathrm{good} \mathrm{heat} \mathrm{dissipation})\hfill \\ R_{initial}^{16}(\mathrm{good} \mathrm{waterproof} \mathrm{effect})\hfill & R_{initial}^{17}(\mathrm{Chip} \mathrm{fluid} \mathrm{is} \mathrm{easy} \mathrm{to} \mathrm{separate})\hfill & R_{initial}^{18}(\mathrm{reasonable} \mathrm{layout})\hfill \end{array}\right\}$$

(23)

4.4. CNC Machine Tool Design Intent Evaluation Based on a Fuzzy Network Cooperative Game

In this study, expert panel members, typical users, and mechanical design professionals were invited to form an evaluation panel to assess the correlation among initial design intents. The specific evaluation process is as follows: First, sample pictures are observed to familiarize them with product characteristics. The correlation between pairs of intent terms is subsequently determined. If a correlation exists, selection is performed according to the fuzzy number evaluation rules; if no correlation exists, a value of 0 is assigned. The experimenters are responsible for summarizing the evaluation results and whitening the fuzzy numbers. On this basis, Formulas (8)–(11) are used to calculate the network degree centrality, betweenness centrality, and closeness centrality of each design intent. The calculation results are shown in

Table 6. Network attribute values of initial CNC machine tool design intents.

Initial Intent Terms	Degree Centrality	Betweenness Centrality	Closeness Centrality
${R_1}_{initial}$	0.882	0.403	0.537
${R_2}_{initial}$	0.882	0.690	0.537
${R_3}_{initial}$	1.000	0.984	1.000
${R_4}_{initial}$	0.765	0.294	0.162
${R_5}_{initial}$	0.824	0.346	0.340
…
${R_{18}}_{initial}$	0.882	0.559	0.537

.

Taking the three network attributes of design intent as game players and employing a cooperative game model, their equilibrium weights are calculated on the basis of Formulas (12)–(17), yielding weights for degree centrality, betweenness centrality, and closeness centrality of 0.3569, 0.3196, and 0.3235, respectively. Furthermore, Formula (18) is applied to calculate the comprehensive evaluation scores for each design intent. The final results are shown in

Table 7. Comprehensive evaluation values for each design intent.

Initial Intent Terms	Comprehensive Eval.	…	Initial Intent Terms	Comprehensive Eval.
${R_1}_{initial}$	0.6173		${R_{13}}_{initial}$	0.3443
${R_2}_{initial}$	0.7090		${R_{14}}_{initial}$	0.9949
${R_3}_{initial}$	0.9949		${R_{15}}_{initial}$	0.5588
${R_4}_{initial}$	0.4194		${R_{16}}_{initial}$	0.7875
${R_5}_{initial}$	0.5147		${R_{17}}_{initial}$	0.8597
${R_6}_{initial}$	0.6384		${R_{18}}_{initial}$	0.6672

.

On the basis of the comprehensive evaluation values of design intents, combined with the enterprise’s innovation development capability, and through discussion with experts, a requirement threshold exceeding 0.7 is determined for selecting design intents as alternative solutions. Thus, the preliminary design intents for this CNC machine tool are derived as R = {high machining accuracy (R1), high-end operating system (R2), grand appearance (R3), superior ergonomic performance (R4), strong brand identity (R5), good protective performance (R6), strong technological sense (R7), good waterproof effect (R8), easy chip fluid separation (R9)}.

4.5. Refined Design Intent Decision-Making for the CKA6180 CNC Machine Tool Based on a Noncooperative Game

On the basis of the current status of the CKA6180 CNC machine tool and the characteristics of horizontal machine tools, a noncooperative game refined design intent matching decision-making model comprising four dimensions is constructed: design intent satisfaction (CM1), novelty (CM2), feasibility (CM3), and relevance (CM4).

• Satisfaction represents the degree to which the design intent aligns with the development trends of existing similar products and can provide guidance for current product design;
• Novelty is the degree of innovativeness of the design intent relative to trends in similar products on the market and the enterprise’s existing products;
• Feasibility represents the extent to which a design intent can be realized in actual product design;
• Relevance represents the degree of correlation between a design intent and actual product design trends.

Expert panel members use the correlation criteria shown in Figure 5 to evaluate the degree of matching of design intents.

The results are averaged to obtain the correlation matrix, as shown in

Table 8. Correlation between design intents and criteria.

Design Intent Terms	Correlation Indicator|Average Correlation
R1	$C{M}_1^1$|3.2	$C{M}_2^1$|2.4	$C{M}_3^1$|3.0	$C{M}_4^1$|2.8
R2	$C{M}_1^2$|3.6	$C{M}_2^2$|4.0	$C{M}_3^2$|3.2	$C{M}_4^2$|3.4
R3	$C{M}_1^3$|4.0	$C{M}_2^3$|3.4	$C{M}_3^3$|3.8	$C{M}_4^3$|4.0
R4	$C{M}_1^4$|3.4	$C{M}_2^4$|2.4	$C{M}_3^4$|3.2	$C{M}_4^4$|2.6
…
R9	$C{M}_1^9$|3.4	$C{M}_2^9$|2.6	$C{M}_3^9$|3.6	$C{M}_4^9$|2.8

.

First, a reliability and validity test was conducted on the questionnaire results, yielding a Cronbach’s α coefficient of 0.815 (greater than 0.8) for reliability and a p-value of 0.026 (less than 0.05) for validity, indicating that the data are stable and reliable. Subsequently, using Formulas (19) and (20), the utility matrix for each design intent is obtained. Thus, according to Formula (21), the comprehensive utility values for each design intent are {0.001, 0.044, 0.101, 0.001, 0.01, 0.135, 0.052, 0.013, 0.005}, i.e., the importance ranking of the initial design intents is: R₆ > R₃ > R₇ > R₂ > R₈ > R₅ > R₉ > R₁ = R₄. On the basis of the data magnitude, initial design intents with comprehensive utility values greater than 0.1 are selected as the final design intents for the CKA6180 CNC machine tool, namely, good protective performance and grand appearance.

4.6. Results Validation

To enhance the credibility of the decision-making results, this study employs the TOPSIS [66] method for validation. As a comprehensive evaluation approach, it determines priority ranking by calculating the distances between the evaluated objects and both the ideal best and ideal worst solutions [67]. The specific algorithmic steps are as follows:

• Construct the normalized matrix. Assume a decision matrix $C={(c_{fg})}_{YV}$ for a multi-attribute decision-making problem involving Y evaluation objects and V evaluation indicators. The normalized matrix $\tilde{E}={({\tilde{e}}_{fg})}_{YV}$ is obtained using the vector normalization method.

  $${\tilde{e}}_{fg}=c_{fg}/\sqrt{{\displaystyle \sum _{f=1}^Y{c}_{fg}^2}},$$

  (24)
• Determine the positive and negative ideal solutions, denoted as ${\tilde{E}}_g^{+}$ and ${\tilde{E}}_g^{-}$, respectively:

  $${\tilde{E}}_g^{+}=\left\{\max ({\tilde{e}}_{11},{\tilde{e}}_{12},\cdots ,{\tilde{e}}_{1V}),\cdots ,\max ({\tilde{e}}_{Y1},{\tilde{e}}_{Y2},\cdots ,{\tilde{e}}_{YV})\right\},$$

  (25)

  $${\tilde{E}}_g^{-}=\left\{\min ({\tilde{e}}_{11},{\tilde{e}}_{12},\cdots ,{\tilde{e}}_{1V}),\cdots ,\min ({\tilde{e}}_{Y1},{\tilde{e}}_{Y2},\cdots ,{\tilde{e}}_{YV})\right\},$$

  (26)
• Calculate the Euclidean distance. The Euclidean distance is employed to measure the distances ${\tilde{D}}_f^{+}$ and ${\tilde{D}}_f^{-}$ between the object indicators and the positive/negative ideal solutions:

  $${\tilde{D}}_f^{+}=\sqrt{{\displaystyle \sum _{g=1}^V\omega ({\tilde{e}}_{fg}-{\tilde{E}}_g^{+})}},$$

  (27)

  $${\tilde{D}}_f^{-}=\sqrt{{\displaystyle \sum _{g=1}^V\omega ({\tilde{e}}_{fg}-{\tilde{E}}_g^{-})}},$$

  (28)
• Calculate the relative closeness of the evaluation objects. The evaluation objects are ranked in terms of importance based on the magnitude of the relative closeness ${\tilde{F}}_f$; the larger the value of ${\tilde{F}}_f$, the more important the evaluation object.

  $${\tilde{F}}_f={\displaystyle \frac{{\tilde{D}}_f^{-}}{{\tilde{D}}_g^{+}+{\tilde{D}}_g^{-}}}.$$

  (29)

Substituting the data from Table 8 into Formulas (24)–(29) yields the evaluation results based on the TOPSIS method, as shown in Table 8.

According to the ranking results shown in

Table 9. TOPSIS evaluation calculation results.

Design Intent Terms	${\tilde{\mathit{D}}}_{\mathit{f}}^{+}$	${\tilde{\mathit{D}}}_{\mathit{f}}^{-}$	${\tilde{\mathit{F}}}_{\mathit{f}}$	Ranking Result
R1	2.408	0.200	0.077	9
R2	1.077	1.844	0.631	3
R3	0.632	2.059	0.765	2
R4	2.417	0.283	0.105	8
R5	1.697	0.980	0.366	6
R6	0.400	2.298	0.852	1
R7	1.166	1.897	0.619	4
R8	1.510	1.149	0.432	5
R9	2.078	0.693	0.250	7

, the top two design intents are R₆ (good protective performance) and R₃ (grand appearance), and the overall ranking order is: R₆ > R₃ > R₂ > R₇ > R₈ > R₅ > R₉ > R₄ > R₁. This result is generally consistent with the findings obtained in this study, thereby confirming the feasibility of the proposed method.

4.7. Results Discussion

This study addresses three research questions: the identification and representation of cognitive agents’ design intents, multi-criteria decision-making, and refined design intent matching. First, based on scenario analysis theory, the initial design intents of users and designers for a certain type of product were respectively obtained, and the results were represented using different approaches. Second, by combining complex network attributes and game theory, a fuzzy network cooperative game model was constructed to complete the multi-criteria evaluation of design intents. Finally, based on the specific research object and incorporating the concept of refined design along with game theory, a noncooperative game refined decision-making model was established to finalize the design intent decision. The feasibility of the proposed method was further verified using the TOPSIS method. The analysis results indicate that for the CKA6180 CNC machine tool, the final determined design intents focus on “grand appearance (0.135)” and “good protective performance (0.101).” In the initial ranking, those with greater attention were mostly functional requirements such as machining accuracy and the operating system, showing a clear difference from the final intents. This change indicates that with the introduction of refined design thinking, the matching results of design intent become more targeted and practically guiding. The reason for this finding is that as a core product of the enterprise, CKA6180 already meets most customer needs well in terms of functional aspects such as machining accuracy and operating systems, and these advantages can be maintained. However, in terms of appearance and form, there is still a gap compared with similar products on the market. Therefore, during product iteration, attention should be given to enhancing appearance styling while also considering the optimization of local functions. This insight suggests that in design research, in addition to focusing on constructing theoretical methods, integration with specific research objects should be emphasized to achieve “symmetry” between theoretical research and actual products, thereby promoting the effective transformation of design from theory to practice.

The study of design intent is a process involving the presentation and interaction of cognitive information among multiple agents, such as users, designers, and enterprise decision-makers. Previous research [68,69] has noted that the cognitive information of cognitive agents often has fuzzy characteristics, forming so-called “cognitive grey boxes”. The interaction among information of multiple agents involves the gradual clarification of these “grey boxes”. The fuzzy network constructed in this paper uses fuzzy number representation to simulate the fuzzy cognitive characteristics of cognitive agents and employs complex networks to establish feature correlations, achieving a leap from perceptual cognition mining to rational visual representation. Simultaneously, leveraging the advantages of game theory in balancing multiagent interests, corresponding game models are constructed for different cognitive stages, multiagent cognitive interaction is systematically completed, a serial and progressive design problem-solving process is formed, “cognitive symmetry” is ultimately achieving, and a methodological reference is provided for subsequent related research.

5. Conclusions

Facing with the fuzzy decision-making problem of design intent for complex products involving multiagent participation, in this paper, a refined decision-making method based on noncooperative–cooperative game serialization is proposed. Considering the design of the CKA6180 CNC machine tool, the feasibility of this method is verified.

5.1. Theoretical Contributions

• A multiagent design intent mining method based on scenario theory is proposed. By placing cognitive agents in corresponding scenarios, the accuracy of design intent identification is improved.
• To address the fuzziness and complexity of multiagent cognitive information, a noncooperative–cooperative game serialization decision-making process is constructed. Corresponding game models are established according to the characteristics of different cognitive stages, achieving inferential decision-making for design intent from “divergence” to “convergence” and increasing evaluation accuracy.
• A refined design intent decision-making mode is proposed. Compared with previous design intent reasoning starting from broad categories, this method combines refined design concepts with a noncooperative game and can reduce the “disturbance” of experience dependence on the design process, thereby improving design satisfaction.

This study innovates from a methodological perspective and theoretically extends the application of game theory in multicriteria decision-making within the product innovation design process. From a computational perspective, the method primarily comprises a cooperative game model for addressing multimodal data coordination and a noncooperative game model for refined decision-making, with the complexity being the superposition of the two-stage results. In terms of scalability, while the current research object is limited to the design intent decision-making of the CKA6180 CNC machine tool, the method possesses universal characteristics and can be extended to the design decision-making of product-related modules in subsequent research.

5.2. Managerial Implications and Application Value

This research constitutes the primary step in product innovation design. It enables the systematic identification and characterization of explicit and implicit requirements from multiple roles, such as users and designers, at the front end of the design process. Consequently, it significantly reduces the waste of design resources caused by cognitive biases and enhances the collaborative efficiency and decision-making quality of interdisciplinary design teams.

Furthermore, this research supports machine tool enterprises in transitioning from “functional stacking” to high-end development characterized by “human-centric and scenario-adaptive” approaches. It provides a design basis for transforming toward a “product + service” system, ultimately improving product user satisfaction, safety, and full life-cycle competitiveness.

6. Limitations and Future Research Directions

6.1. Research Limitations

This study constructed a refined decision-making method for the multimodal fuzzy design intent of complex products based on noncooperative–cooperative game serialization. It mined the design intents of agents such as users and designers from a combined qualitative and quantitative perspective, thereby clarifying the design direction for the CKA6180 CNC machine tool. However, this study still includes the following limitations:

• Cognitive agents were only defined as users and designers. However, in the actual product life cycle, cognitive agents also include engineers, decision-makers, product recyclers, etc. Whether this method can analyze higher-dimensional information from the perspective of more cognitive agents to facilitate design intent decision-making remains to be verified.
• At present, the proposed method is employed solely for the representation and evaluation of the current data. Future work should consider expanding the data dimensions-for instance, by incorporating evaluative data from additional cognitive agents such as engineers and enterprise managers, as well as introducing more fine-grained constraints specific to the research object-in order to further examine the computational complexity and scalability of the method.
• The research data were derived solely from qualitative acquisition and evaluation. Future considerations should include data acquisition and analysis methods that combine qualitative and quantitative approaches from multiple perspectives, such as physiological, psychological, and behavioural measurements.

6.2. Future Research Directions

In the future, artificial intelligence technology can be utilized to construct intelligent agent models for corresponding cognitive agents, including engineers and decision-makers. Qualitative and quantitative methods can be integrated to further increase the efficiency of design intent identification. Additionally, during the design intent evaluation stage, physiological measurement and other technologies can be introduced to collect implicit data, expand evaluation dimensions, and further improve decision-making accuracy.