## 1 Introduction
tackled the issues of subjectivity, uncertainty, and heterogeneity in decision semantics during the conceptual design phase by proposing a decision-making method that incorporates multi-granularity heterogeneous evaluation semantics under uncertainty. This method transforms multi-granularity heterogeneous semantics into a cloud model decision matrix and constructs an advantage matrix using random numbers based on the cloud model distribution. Finally, the VIKOR model is employed to select the optimal scheme [18]. [PERSON] et al. proposed a quantitative evaluation method based on Rough Sets to address the issue of ambiguity in user emotional expression. This method reduces uncertainty in the evaluation process to identify product features and user experiences that require improvement. The effectiveness of the proposed method was demonstrated through a case study involving a wireless vacuum cleaner [19]. [PERSON] et al. proposed a multi-criteria decision model for product design schemes based on TOPSIS-MOGA to address the issues of decision continuity and integration throughout the design phase. This model ensures continuity in the decision-making process by integrating decision criteria and employs the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), utilizing hesitant fuzzy linguistic term sets and the entropy weight method to select the optimal conceptual design scheme [20]. [PERSON] et al. aimed to reduce reliance on subjective judgments of designers in product design decision-making by introducing a data-driven method that employs an ideal scheme ranking method, the entropy weight method for weighting decision criteria, and the Borda count method for aggregating decision information [21]. [PERSON] et al. addressed the generation and decision-making of green design schemes throughout the product lifecycle, proposing a multi-attribute decision-making method based on Composite Weighting, TOPSIS, and gray relation analysis, optimizing green design schemes [22]. [PERSON] et al. discussed the effective integration of Multi-Phase Product Design Decision-Making, proposing a nonlinear fusion method that converts decision-makers' linguistic judgments into three-parameter interval gray number scales, using the interval Analytic Hierarchy Process to calculate weights and support the optimal selection of schemes through the Plant Growth Simulation Algorithm (PGSA) [23]. [PERSON] et al. proposed a conceptual design evaluation method based on Z-numbers to address the issues of uncertainty and subjectivity in the decision-making process. They employed the fuzzy Analytic Hierarchy Process (Z-AHP) under Z-number conditions to determine indicator weights and ultimately evaluated design schemes using the Z-Technique for Order of Preference by Similarity to Ideal Solution (Z-TOPSIS), thereby optimizing the conceptual design schemes [24]. [PERSON] et al. proposed a systematic design decision-making method that utilizes PFA theory as a data collection tool and employs Structural Equation Modeling (SEM) to validate the model. They then integrated path load normalization with the Analytic Hierarchy Process (AHP) for a comprehensive evaluation of product schemes, using a machine tool product design as a case study to verify the reliability of the method [25]. [PERSON] et al. utilized Interval-valued Intuitionistic Fuzzy Numbers (IVIFNs) for attribute evaluation and developed an aggregation operator to construct the Fuzzy Synthetic Decision Matrix (PSDM) using the Karnik-Mendel algorithm. They then combined interval-valued intuitionistic fuzzy cross-entropy with the TOPSIS framework to rank the candidate schemes [26]. The above studies provide multiple approaches to the decision-making issues in product design schemes. However, existing research primarily focuses on the expression and processing of evaluative information from decision-makers and the integration of multi-stage decision data. Few studies integrate user preferences with expert evaluations in product design decision-making.