Some Novel Maclaurin Symmetric Mean Operators for q-Rung Picture Fuzzy Numbers and Their Application to Multiple Attribute Group Decision Making

Abstract

q-rung picture fuzzy sets can express fuzzy information and simulate realistic decision-making problem scenarios more accurately through the assignment of variable parameter q. Considering that Schweizer–Sklar t-conorm and t-norm (SSTT) has strong flexibility in the procedure of data fusion and Maclaurin symmetric mean MSM operator is able to consider the relevance between multi-parameters, multi-attributes and even multi-decision-makers in the multiple attribute group decision-making (MAGDM) problems. Therefore, in this paper, we expand SSTT to q-rung picture fuzzy numbers (q-RPFNs) and define Schweizer–Sklar operational rules for q-RPFNs. Then we amalgamate the MSM operator with Schweizer–Sklar operations, and advance the q-rung picture fuzzy Schweizer–Sklar Maclaurin symmetric mean (q-RPFSSMSM) operators, the q-rung picture fuzzy Schweizer–Sklar generalized Maclaurin symmetric mean (q-RPFSSGMSM) operators, the q-rung picture fuzzy Schweizer–Sklar weighted Maclaurin symmetric mean (q-RPFSSWMSM) operators and the q-rung picture fuzzy Schweizer–Sklar weighted generalized Maclaurin symmetric mean (q-RPFSSWGMSM) operators. Subsequently, we design a novel method based on the developed operators and use an illustrated example to explain how successful it is. In the end of this study, to demonstrate the excellence and accessibility of our proposed method, a comparison analysis with other methods is conducted.

Keywords

• q-rung picture fuzzy set
• Schweizer–Sklar t-norm and t-conorm
• Maclaurin symmetric mean operator
• multiple attribute group decision making (MAGDM)