Pythagorean picture fuzzy sets, part 1 – basic notions

Abstract

Picture fuzzy set (2013) is a generalization of the Zadeh' fuzzy set (1965) and the Anta-nassov' intuitionistic fuzzy set. The new concept could be useful for many computational intelligent problems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10, 11]. New concept - Pythagorean picture fuzzy set (PPFS) is a combination of Picture fuzzy set with the Yager's Pythagorean fuzzy set [12, 13, 14]. First, in the Part 1 of this paper, we consider basic notions on PPFS as set operators of PPFS's, Pythagorean picture relation, Pythagorean picture fuzzy soft set. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picture negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS. As a result we will have a new branch of the picture fuzzy set theory.