Algorithm for Multiple Attribute Decision-Making with Interactive Archimedean Norm Operations Under Pythagorean Fuzzy Uncertainty

Recently, a great attention is paid toward developing aggregation operators for Pythagorean fuzzy set (PFS). However, few of them have adopted the rules of Archimedean t-conorm and t-norm (ATT) to aggregate the numbers. Motivated by this, the keep interest of the present work is to define some Pythagorean fuzzy interaction aggregation operators with the aid of ATT. To do this, the objective of the work is divided into three folds. In the first fold, we define some interactive operations law for PFSs and propose their corresponding new interaction Pythagorean operators, namely Archimedean based Pythagorean fuzzy interactive weighted averaging (A-PFIWA) operator and Archimedean based Pythagorean fuzzy interactive weighted geometric (A-PFIWG) operator. In the second fold, we investigate their desirable properties and study the several special cases of the proposed ones with respect the existing ones. Lastly, we design an algorithm to solve the multiple attribute decision-making issues with Pythagorean fuzzy uncertainties and explain their utilization with a numerical example. Further, several examples are discussed to demonstrate the validity and superiority of the proposed method. The novelties of proposed operators are that they not only can offer a more flexible method via selecting diverse forms of ATT, but also can reflect the interactive influence among membership degree and nonmembership degree for PFSs. (C) 2021 The Authors. Published by Atlantis Press B.V.

Automated summary

This article focuses on defining Pythagorean fuzzy interaction aggregation operators with the aid of Archimedean t-norm and t-conorm rules, discussing their definition, properties, and applications through three main aspects.