## 1 Introduction
The resulting assessment data will then be adopted to model the PSS evaluation process and determine the optimal solution [15]. [PERSON] [16] constructed a five-step iterative process to support decision making in PSS design, which matches CV with sustainability to ensure customer satisfaction and meet performance requirements. [PERSON] et al. [17] used a refined QFD tool to convert customer requirements into engineering characteristics and ranked these characteristics by importance. Owing to the increasing complexity of PSS evaluation challenges, several multiple-criteria decision models have been adopted to extract the overall value of PSS conceptual solutions, such as the technique for order of preference by similarity to ideal solution (TOPSIS) [14; 18], visekriterijumska optimizacija i kompromisno resenje (VIKOR) [19; 20], and the preference ranking organization method for enrichment evaluation (PROMETHEE) [21]. For instance, [PERSON] and [PERSON] [22] adopted the fuzzy AHP and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) to evaluate PSS designs and analyze the benefit and operational risks in converting a product-focused business into a service-oriented operation. [PERSON] et al. [23] proposed a modified rough vlsekriterijumska optimizacija i kompromisno resenje (VIKOR) model to reconcile the effects of objective design and subjective preferences on conceptual solution evaluations, thereby enhancing the objectivity of the design concept evaluation. Furthermore, it can be determined that the aforementioned method can transform multiple evaluation criteria into a single objective, as well as calculate the comprehensive utility of the solution using this objective. However, the disparity between CV and economic interests is rarely discussed in previous studies [15]. In most cases, CV is simply considered an ordinary design requirement (such as weight, price, or power)when assessing the optimality of a conceptual solution. Considering the competing relationship between customer needs and economic goals, one needs to weigh the design benefit conflicts between product economics and customer needs, and to satisfy product service quality as much as possible while reducing the burden of service transformation in the enterprise, which further promotes our research motivation. To address this issue, this study focuses on balancing the effects of CV and economic requirements on the overall design of a PSS, by considering this process as a cooperative game. It is well-understood that the balancing problem implies that it is impossible for a PSS decision to maximally satisfy all requirements, as the relative importance of CV and economic objectives must be considered to form a balanced solution. Therefore, the multi-objective balancing process resembles cooperative game theory [11; 24], which attempts to obtain an optimal compromise by balancing the interests of all design objectives [25]. Moreover, the utility functions used in cooperative game theory are suitable for the incomplete and fuzzy nature of the early PSS design phase, as they do not require precise inputs and outputs. Inspired by this idea, a conceptual scheme decision approach integrating rough sets and Shapley value for product-service system considering CV-economic objective trade-off is proposed. Compared with previous decision-making methods for PSS design, the main contributions of this study are summarized as follows:  
1. The best worst method (BWM) and entropy weight method are integrated to consider the personal preference and objective weight of the evaluation criteria, and to realize the accurate calculation of the weight. 2. The Shapley value method is proposed to weigh the requirement conflict between the CV and economic objectives, and then the optimal expectation ratio for the two objectives is solved to determine the scheme with optimal overall interests. 3.