Neutrosophic Z-number Schweizer–Sklar prioritized aggregation operators and new score function for multi-attribute decision making

Abstract

Multi-attribute decision making (MADM) is an important branch of modern decision science and has been applied to many real-world scenarios. As decision scenarios become more complex and multidimensional with time, the neutrosophic Z-number can effectively represent this kind of complex and fuzzy information. On the one hand, it takes into account the uncertain, inconsistent and discontinuous information existing in the MADM environment, and on the other hand, it covers the reliability measure of the evaluation information to enhance the credibility of the decision. In the decision process, it will be necessary to consider the flexibility of information fusion and the existence of priority relationships between decision attributes in order to extend the decision processing performance of the neutrosophic Z-number. To this end, based on the features of Schweizer–Sklar t-norm and t-conorm to improve the flexibility and utility of the aggregation process through parameter variations, neutrosophic Z-number Schweizer–Sklar operation laws are proposed. Furthermore, in order to address the features of attributes with linear priority relationships, the advantages of prioritized aggregation operators are considered in the face of this situation. We proposed neutrosophic Z-number Schweizer–Sklar prioritized aggregation operators including the following neutrosophic Z-number Schweizer–Sklar prioritized weighted averaging (NZNSSPRWA) operators and neutrosophic Z-number Schweizer–Sklar prioritized weighted geometric (NZNSSPRWG) operators and the related theorem is proved. Further, the original score function of neutrosophic Z-numbers appears to be incompetent in dealing with more complex and difficult situations, which motivates us to propose a new score function for neutrosophic Z-numbers to effectively enhance the differentiation and ensure the reliability of the decision results. In order to illustrate the methodology, this paper considers and solves MADM problems related to the location of Internet data centres, and in order to demonstrate the effectiveness and practicality of the proposed methodology, a sensitivity analysis of the parameters as well as a discussion of the developed methodology in comparison with the existing methodologies are carried out. The results show that the proposed MADM approach balances the decision attribute priority preferences with the strong flexibility required in practical applications. The developed technique can significantly improve the accuracy and reliability of decisions in complex and changing decision environments and bring the decision process closer to the real needs.