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.
Highlights
Fuzzy set theory proposed by Zadeh [1] is an extension of classical set theory
Naz et al [30] presented the notion of Pythagorean fuzzy graphs (PyFGs), an extension of the concept of Akram and Davvaz’s intuitionistic fuzzy graphs (IFGs), including its applications in decision-making
As fuzzy graph theory can deal with ambiguous and vague notions in a natural way, and has a large number of applications in modeling such real-life systems where the levels of information inherent in the system varies with different levels of precision
Summary
Fuzzy set theory proposed by Zadeh [1] is an extension of classical set theory. Zadeh’s remarkable idea has found many applications in several fields, including chemical industry, telecommunication, decision theory, networking, computer science, and management science. Atanassov [2] introduced the intuitionistic fuzzy set (IFS) as an extension of fuzzy set (FS) theory He broadened the idea of FSs by defining the truthness degree (α) alongside the falseness degree (β) with the requirement 0 ≤ α + β ≤ 1. Ashraf et al [17] presented the notion of SFSs with applications in decision making problems. Another extension suggested by Li et al [18] in 2018 is the q-rung picture fuzzy set (q-RPFS). Naz et al [30] presented the notion of Pythagorean fuzzy graphs (PyFGs), an extension of the concept of Akram and Davvaz’s IFGs, including its applications in decision-making. We describe an application of SFGs in the decision making process
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