Spherical Fuzzy Graphs with Application to Decision-Making

Abstract

In a network model, the evaluation information given by decision makers are occasionally of types: yes, abstain, no, and refusal. To deal with such problems, we use mathematical models based on picture fuzzy sets. The spherical fuzzy model is more versatile than the picture fuzzy model as it broadens the space of uncertain and vague information, due to its outstanding feature of vast space of participation of acceptable triplets. Graphs are a mathematical representation of networks. Thus to deal with many real-world phenomena represented by networks, spherical fuzzy graphs can be used to model different practical scenarios in a more flexible manner than picture fuzzy graphs. In this research article, we discuss two operations on spherical fuzzy graphs (SFGs), namely, symmetric difference and rejection; and develop some results regarding their degrees and total degrees. We describe certain concepts of irregular SFGs with several important properties. Further, we present an application of SFGs in decision making.

Spherical fuzzy graph

“…Definition 2.1. [1] Let V be the non-empty set possess spherical fuzzy graph SFG is G = (P, Q), here P and Q are spherical fuzzy set and spherical fuzzy relation on V in such…”

“…Pythagorean fuzzy graphs generalized out of intuitionistic fuzzy graph [6] and the spherical fuzzy graph acquainted by Akram et. al., [1]. In this paper, spherical fuzzy subgraph, complete spherical fuzzy graph, minimum and maximum degrees of spherical fuzzy graphs are demonstrated.…”

Picture Fuzzy Incidence Graphs with Application

“…Size and order analogous to crisp graphs in FGs were examined by Gani and Ahamed [25]. Akram et al [5] discussed spherical FGs with application to decision-making. Al-Hawary [7] proposed the notion of complete FG.…”

Multi-Criteria Group Decision-Making Using Spherical Fuzzy Prioritized Weighted Aggregation Operators

“…Kahraman et al [9] applied the spherical fuzzy TOPSIS method to find the solution of a problem which is related to the selection of hospital location. Akram et al [10] studied the notion of SFS by providing the solution of a DM problem and Akram [11] presented a DM method based on spherical fuzzy graphs.…”