Abstract
The notion of fuzzy set is introduced to deal with uncertainty, whereas the conventional sets are used for certainty. The extensions of fuzzy set theory such as intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFS) were introduced to overcome drawbacks in fuzzy theory. Fuzzy graph structure is used to deal with the uncertainty in a network and describe its relation on the nonempty vertex set. One of the extensions of intuitionistic fuzzy digraph (IFDG) is Pythagorean fuzzy digraph (PyFDG). IFDG cannot handle if the sum of degree of acceptance and degree of rejection for an arc weight exceeds 1. So, we introduced PyFDG to overcome the limitations in IFDG and it deals with the imprecise arc weight involving degree of acceptance and degree of rejection. Pythagorean fuzzy digraph (PyFDG) and its basic operations and score function of PyFDG are defined in this paper. Algorithm is proposed to solve application problem in healthcare center.
Highlights
Fuzzy set is unlike ordinary set whose elements of a set have membership value
We introduced Pythagorean fuzzy digraph (PyFDG) to overcome the limitations in intuitionistic fuzzy digraph (IFDG) and it deals with the imprecise arc weight involving degree of acceptance and degree of rejection
Definition of intuitionistic fuzzy set (IFS) is a generalized fuzzy set whose elements of a set have both membership and nonmembership value and it is introduced by Atanassov [5,6,7]. e concepts of intuitionistic fuzzy relations (IFR) and intuitionistic fuzzy graph (IFG) are the generalizations of fuzzy graphs (FG) and it is developed by Shannon and Atanassov [8]
Summary
Fuzzy set is unlike ordinary set whose elements of a set have membership value. It is found by Zadeh [1] in the year 1965. Definition of IFS is a generalized fuzzy set whose elements of a set have both membership and nonmembership value and it is introduced by Atanassov [5,6,7]. Notion of maximal product of two PyFGs, residue product of two PyFGs, and its properties have been introduced and studied by Akram et al [32] He et al [33] combined Pythagorean 2-tuple linguistic fuzzy set and QUALIFLEX method. Zhang et al [17] combined the novel TODIM along with cumulative prospect theory under 2-tuple linguistic Pythagorean fuzzy sets (2TLPFS) and basic definitions and operators of 2-TLPFSs introduced by Zhang et al [34]. E objective of our work in this paper is to introduce some operations on Pythagorean fuzzy digraph, decisionmaking algorithm for solving problem using the notion of Pythagorean fuzzy digraph.
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