The Properties of Continuous Pythagorean Fuzzy Information

Abstract

In practical decision‐making processes, we can utilize various types of fuzzy sets to express the uncertain and ambiguous information. However, we may encounter such the situations: the sum of the support (membership) degree and the against (nonmembership) degree to which an alternative satisfies a criterion provided by the decision maker may be bigger than 1 but their square sum is equal to or less than 1. The Pythagorean fuzzy sets (PFS), as the generalization of the fuzzy sets, can be used to effectively deal with this issue. Therefore, to enrich the theory of PFS, it is very necessary to investigate the fundamental properties of Pythagorean fuzzy information. In this paper, we first describe the change values of Pythagorean fuzzy numbers (PFNs), which are the basic components of PFSs, when considering them as variables. Then we divide all the change values into the eight regions by using the basic operations of PFNs. Finally, we develop several Pythagorean fuzzy functions and study their fundamental properties such as continuity, derivability, and differentiability in detail.

TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making

“…In the future, the application of the proposed models and methods of SVNSs and INSs needs to be explored in the decision making [86][87][88][89][90][91][92][93][94][95][96][97][98][99], risk analysis and many other uncertain and fuzzy environment [100][101][102][103][104][105][106][107][108][109][110][111][112].…”

Pythagorean Fuzzy Information Measures and Their Applications

“…Meanwhile, inspired by soft set theory and linguistic set theory, they proposed Pythagorean fuzzy soft sets and Pythagorean fuzzy linguistic sets, respectively. Gou et al . developed several Pythagorean fuzzy functions and investigated their fundamental properties such as continuity, derivability, and differentiability in detail.…”

New Operations for Interval-valued Pythagorean Fuzzy Set

“…The PFS has been investigated from different perspectives, including decision making technologies [5][6][7][8][9][10][11][12][13], aggregation operators [14][15][16][17][18][19][20][21][22], information measures [23][24][25] , the extensions of PFS [26][27][28][29][30][31], fundamental properties [32][33][34]. In particular, an extension of PFS named interval-valued Pythagorean fuzzy set (IVPFS) [10,21] is a hot topic at present [35].…”