Abstract
A Pythagorean fuzzy set (PFS) is a powerful tool for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to an intuitionistic fuzzy model. This paper proposes a new graph, called Pythagorean fuzzy graph (PFG). We investigate some properties of our proposed graphs. We determine the degree and total degree of a vertex of PFGs. Furthermore, we present the concept of Pythagorean fuzzy preference relations (PFPRs). In particular, we solve decision-making problems, including evaluation of hospitals, partner selection in supply chain management, and electronic learning main factors evaluation by using PFGs.
Highlights
Since Zadeh’s seminal work [1], the classical logic has been extended to fuzzy logic, which is characterized by a membership function in [0, 1] and provides a powerful alternative to probability theory to characterize imprecision, uncertainty, and obscureness in various fields
We have introduced a new concept of Pythagorean fuzzy graph (PFG)
We have developed a series of operational laws of PFGs and investigated their desirable properties in detail
Summary
Since Zadeh’s seminal work [1], the classical logic has been extended to fuzzy logic, which is characterized by a membership function in [0, 1] and provides a powerful alternative to probability theory to characterize imprecision, uncertainty, and obscureness in various fields. To capture more useful information under imprecise and uncertain circumstances, Yager [4,5,6] recently proposed the concept of Pythagorean fuzzy set (PFS) as a new evaluation format, which is characterized by the membership and the non-membership degree satisfying the condition that their square sum is not greater than 1. For this case, the PFS shows its wider applicability than the IFS. Generalized the concept of fuzzy graphs to IFGs. Naz et al [19,20] discussed some basic notions of single valued neutrosophic graphs along with its application in multi criteria decision-making. We solve decision-making problems, including evaluation of hospitals, partner selection in supply chain management, electronic learning main factors evaluation by using PFGs
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