Maclaurin Symmetric Mean-Based Archimedean Aggregation Operators for Aggregating Hesitant Pythagorean Fuzzy Elements and Their Applications to Multicriteria Decision Making

Abstract

Due to larger capacity to deal ambiguous, imprecise, and vague information, hesitant Pythagorean fuzzy sets are now being extensively used in multicriteria decision making contexts. The main objective of this chapter is to combine Maclaurin symmetric mean with Archimedean $t$-conorms and $t$-norms to aggregate hesitant Pythagorean fuzzy elements. In multicriteria decision making, it is frequently required to consider heterogeneous interrelationships among the decision values provided by the decision makers. To handle those types of heterogeneous characteristics, Maclaurin symmetric mean operator is used for aggregating multi-input hesitant Pythagorean fuzzy arguments. At the same time, Archimedean $t$-conorms and $t$-norms are used to produce adaptable and flexible operational rules for fuzzy numbers. Thus, the proposed aggregation operators not only capture interrelationships between the input arguments but also efficient to construct several forms of aggregation operators by resolving hesitant Pythagorean fuzzy uncertainties. In the proposed method, at first, some operational rules of hesitant Pythagorean fuzzy elements are defined based on Archimedean $t$-conorms and $t$-norms. Then using those rules, Archimedean hesitant Pythagorean fuzzy Maclaurin symmetric mean aggregation operators and their weighted forms are developed. Some classifications and properties related to the proposed operators are discussed. By employing those operators, an approach for solving multicriteria decision making problems is developed. Finally, a numerical example is provided to verify the feasibility, practicality, and effectiveness of the proposed approach.