Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues

The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of Hamacher t-norm and t-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectiveness. We investigate the impact of the parameter for different values on decision-making outcomes. The main advantage of utilizing the suggested operator lies in the fact that this operator provides an increasingly complete perspective on the issue to the decision-makers. The technique suggested in this study gives progressively broad, improve the accuracy and exact outcomes when contrasted with the existing related methods. Therefore, this technique performs an important function in real-life MADM issues.