Interval-valued hesitant Pythagorean fuzzy Archimedean aggregation operators and their application to multicriteria decision-making

In the context of multicriteria decision making (MCDM), it is frequently observed that the representation of cognitive information may not always be sufficient using hesitant Pythagorean fuzzy set (HPFS). From this perspective, the interval-valued hesitant Pythagorean fuzzy (IVHPF) set is more flexible than HPFS to capture the cognitive versatility of decision makers. Again, Archimedean -conorm and -norms (At-CN&t-Ns) possess the efficient capability to generate versatile and flexible operational rules for fuzzy numbers. Utilizing the benefit of A-CN&-Ns some basic operations are introduced to aggregate IVHPF elements so that many other kinds of -conorm and -norms t(t-CN&t-Ns), such as algebraic, Einstein, Hamacher, Dombi, Frank and other classes of t-CN&-Ns can be generated. Based on those concepts, several forms of aggregation operators, viz., weighted averaging, weighted geometric, ordered weighted averaging and ordered weighted geometric aggregation operators, are updated in the IVHPF environment. Conversion processes from A-CN&-Ns based aggregation operators to other variants are also discussed. Using the proposed operators, a methodology for solving MCDM problems with IVHPF cognitive information is proposed. To explore the applicability of the proposed approach, two examples are considered and solved. Results obtained from this method are compared with the existing approaches to establish the efficiency of the proposed method.