Power Aggregation Operators of Interval-Valued Atanassov-Intuitionistic Fuzzy Sets Based on Aczel–Alsina t-Norm and t-Conorm and Their Applications in Decision Making

Abstract

Aczel–Alsina t-norm and t-conorm are important t-norm and t-conorm, and they are extended from algebraic t-norm and t-conorm. Obviously, Aczel–Alsina t-norm and t-conorm are more general than some existing t-norm and t-conorm. Furthermore, the power aggregation (PA) operator is also a very famous and valuable operator which can consider the power relation between any two input parameters. In addition, Interval-valued Atanassov-intuitionistic fuzzy set (IVA-IFS) can easily express uncertain information. In order to fully use their advantages, in this analysis, we extend the PA operators based on Aczel–Alsina t-norm and t-conorm to IVA-IFS and propose the interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power averaging (IVA-IFAAPA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered averaging (IVA-IFAAPOA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power geometric (IVA-IFAAPG) and interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered geometric (IVA-IFAAPOG) operators. Moreover, we discuss the properties of the presented operators such as idempotency, monotonicity, and boundedness. In addition, a multi-attribute decision-making (MADM) procedure is proposed to process the IVA-IF information. Finally, a practical example is used to show the effectiveness and superiority of the proposed method by comparing it with some existing operators.