## 2 Research on PSS Design Evaluation  
When a manufacturer initially transitions from a product-focused approach to PSS, they are more likely to encounter design issues or accidents owing to a lack of service design knowledge. Simultaneously, various feasible PSS concepts are usually generated during the early design stage [12], and the selection of design concepts directly affects the service performance of the PSS concepts. Therefore, how to evaluate and rank the PSS design concepts and provide a most suitable design for the detailed design is still a critical issue in the scientific field of PSS. Previously, [PERSON] et al. [26] conducted a systematic review of the PSS literature, and analyzed PSS evaluation methodologies from the perspectives of CV and sustainability and their trade-offs. [PERSON] and [PERSON] [27] proposed an importance-performance analysis (IPA) method based on [PERSON]'s model to evaluate the importance of CV; in addition, they employed vague sets to handle the uncertainty of PSS evaluations. Presently, studies on PSS concept evaluation generally focus on two areas: (1) PSS criteria weighting based on customer requirements, and (2) the objective aggregation of PSS assessment information. Because PSS concept evaluation is a multiple-criteria decision analysis problem, accurate criteria weights are crucial for the efficacy of this process. Accordingly, various weighting methods have been proposed to obtain accurate criteria weights. For instance, [PERSON] et al. [28] used a combination of ANP and niche theory to quantify customer perceptions of value throughout the customer experience cycle, as well as facilitate the selection of PSS concepts. To help designers to select optimal PSS designs, [PERSON] et al. (2019) presented a method that adopts the decision-making trial and evaluation laboratory (DEMATEL) model to determine influence weights between design attributes, including the VIKOR method to determine the gap between a conceptual solution and the ideal solution. The aforementioned methods (including ANP and DEMATEL) all rely on the construction of several judgment matrices and a large number of pair-wise comparisons. Consequently, with several criteria, these methods often fail to obtain accurate and objective criteria weights. On this basis, BWM, a new multi-criteria decision-making method, was proposed by Professor [PERSON] (2018), based on the idea of pairwise comparison to complete the calculation of criteria weight. Additionally, the advantage of BWM is to construct a structured comparison method rather than any two criteria pairwise comparison ([PERSON] and others, 2018). However, because the aforementioned subjective weighting methods consider subjective judgments of the DM, it is inevitable that the resulting criteria weightings will be strongly biased by the personal preferences of the DM. Hence, the entropy weight method (EWM) was implemented in our research to correct the subjective weightings of each criterion, and to construct a comprehensive weighting function that ensures objectivity in the evaluation of PSS conceptual solutions. In the early stages of PSS development, quantitative data on customer needs and values are usually unavailable, and the uncertainty in decision analysis data often triggers invalid or inaccurate evaluations. In several studies, fuzzy models have been adopted to improve the accuracy of decision analysis, such as intuitionistic fuzzy sets, fuzzy set theory, and rough set theory have been proposed to capture uncertainty evaluation information. Fuzzy analysis does not require quantitative input from DMs, but can obtain initial evaluation information by predetermined membership function, and transform it into scheme evaluation data. For instance, [PERSON] et al. (2019) used fuzzy random variables to address uncertainties in PSS concept evaluation data, and ranked PSS conceptual solutions using the information axiom (i.e., minimize information content). [PERSON] et al.