Possibility Fermatean Interval Valued Fuzzy Soft Set and Their Application to Decision Making Framework

In this paper, we introduce the theory of possibility Fermatean interval valued fuzzy soft (PFIVFS) set and its application to real life problems. The PFIVFS set is a generalization of Pythagorean fuzzy soft and soft set. We define some operations consist of complement, union, intersection, AND and OR. Notably, we show DeMorgan’s laws and associative laws and distributive laws are valid in PFIVFS set theory. We discuss the need to buy a laptop and find several stages for consumer goes through before purchasing a product. We propose an algorithm to solve the decision making problem based on soft set method. To compare PFIVFS set and Fermatean interval valued fuzzy soft (FIVFS) set for dealing with decision making problems, we find a similarity measure. Finally, an illustrative example is discussed to prove that they can be effectively used to solve problems with uncertainties.