Pythagorean picture fuzzy sets: Part 2-some main picture logic operators and picture inference processes

Abstract

Pythagorean picture fuzzy set (PPFS) is a combination of picture fuzzy set and the Yager’s Pythagorean fuzzy set [12–14]. In the first part of the paper [17] we introduced some basic notions namely the set operators on PPFS. The missing part in our previous work is defining the extension of such the operators on the Spherical fuzzy set toward applications of multiattribute group decision making problems. In this second part, we will tackle this issue and present some main operators on PPFS such as the picture negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS. Lastly, the compositional rule of inference in PPFS is presented accompanied with a numerical example.