Picture fuzzy sets - A new concept for computational intelligence problems

Abstract

Abstract-Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov) . Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.

HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis

“…A Picture Fuzzy Set (PFS) (Cuong & Kreinovich, 2013) in a non-empty set X is, where l_ A ðxÞ is the positive degree of each element x 2 X; g_ A ðxÞ is the neutral degree and c_ A ðxÞ is the negative degree satisfying the constraints, l_ A ðxÞ; g_ A ðxÞ; c_ A ðxÞ 2 ½0; 1; 8x 2 X; ð27Þ 0 6 l_ A ðxÞ þ g_ A ðxÞ þ c_ A ðxÞ 6 1; 8x 2 X:…”

Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

“…Picture fuzzy set (PFS), early introduced by Cuong, 1,2 is a generalization of the concept of intuitionistic fuzzy set (IFS) that assigns to each element a positive membership degree, a neutral membership degree, and a negative membership degree. PFS has only one constraint—the sum of all degrees must not exceed 1.…”

A classification of representable t-norm operators for picture fuzzy sets

“…In 2013, a new concept -"picture fuzzy sets" -a direct generalization of Zadeh' fuzzy sets and Atanassov' intuitionistic fuzzy sets were introduced. Then new operators of picture fuzzy sets were presented with many properties were given in [5,6]. In [7], we have introduced picture fuzzy logic connectives and some properties of picture fuzzy sets.…”

“…In this paper, following the research in [5,6], we investigate basic picture fuzzy logic connectives: negation, conjunction, disjuction. A definition and some properties of picture fuzzy negators, picture fuzzy t-norms, picture fuzzy t-conorms are represented in Section 2.…”

“…Some results of the classifications of fuzzy logics operators for fuzzy sets are given in [3,4]. In 2013, we defined the picture fuzzy sets [5,6] and in 2015 some representable t-norms operators and t-conorms operators were defined and firstly were presented in [7,8]. In this paper, we will investigate the classification of representable picture t-norms and picture t-conorms operators for picture fuzzy sets.…”