Preference-based multi-attribute decision-making method with spherical-Z fuzzy sets for green product design

Green product design, i.e., design that harmonizes with the environment, is a crucial component for addressing environmental considerations in the earliest stages of the product life cycle, e.g., new energy vehicles (NEVs), that minimize negative environmental impacts. The designs can encompass material selection, resource use, production requirements, recycling, reuse and the disposal of products. Selecting the optimal design alternative considering multiple attribute indices, e.g., environmental indicators and functional indicators, is a typical multi-attribute decision-making (MADM) problem. This study proposes a hybrid preference-based MADM method with spherical-Z fuzzy numbers (SZFNs) for solving the green product design fuzzy information problem. SZFNs are designed to mine the internal hidden information of traditional Z-numbers, and they combine the characteristics of the reliability constraints of Z-numbers and the advantages of spherical linguistic sets. The operation, aggregation operators and probabilistic measure method of SZFNs are defined in this study. The weight vector of the criteria is obtained by adopting the degree of possibility of spherical-Z (DPSZ). The hybrid MADM method is developed by incorporating the total utility of spherical-Z, which is used to convert the internal meaning of the evaluation information into an additive ratio assessment using gray relation analysis (ARAS-GRA) to obtain the optimal alternative. Finally, a case study, i.e., five green product design schemes for NEVs, is adopted to verify the effectiveness and robustness of this proposed method. A comparative analysis, sensitivity analysis and comprehensive discussion are conducted in this research. The results confirm that this proposed method has an improved performance, and provides some references for designers.