Ordering of interval-valued Fermatean fuzzy sets and its applications
The concept of interval-valued Fermatean fuzzy sets is introduced and some Mathematical operations on the class of IVFFSs are established and the IVFFTOPSIS method for solving multi-criteria decision-making problems is established.
Abstract
Fermatean fuzzy sets (FFSs) introduced by Senapati and Yager (2019) can handle the problems with imprecise and incomplete information more effectively than that of intuitionistic fuzzy sets introduced by Atanassov (1986). Senapati and Yager (2019) have established some basic Mathematical operations over the Fermatean fuzzy sets. They have also introduced the concept of score and accuracy function on the class of Fermatean fuzzy sets for comparing any two arbitrary FFSs. In this paper, firstly, we introduce the concept of interval-valued Fermatean fuzzy sets and establish some Mathematical operations on the class of IVFFSs. Secondly, we introduce various score functions in the class of IVFFSs and study their properties. Thirdly, we compare different ranking methods with the proposed score functions for showing the efficacy of the proposed score functions. Fourthly, we establish the interval-valued Fermatean fuzzy TOPSIS (IVFFTOPSIS) method for solving multi-criteria decision-making problems. Finally, we show the applicability of proposed score functions on IVFFSs and the IVFFTOPSIS method in solving MCDM problems using numerical examples.