Abstract
Based on picture fuzzy sets (PFSs), we use a mathematical model to tackle such types of problems when a person has opinions like yes, no, abstain, and refusal. The spherical fuzzy model is more flexible and practical than the picture fuzzy model, as it enhances the space of uncertainty. It broadens the space of vague information evaluated by decision makers since graphs are the pictorial representation of information. Graphs are a tool to represent a network. To handle some real-world problems, spherical fuzzy graphs can be used more effectively as compared to picture fuzzy graphs (PFGs). In this article, we expand the notion of fuzzy Zagreb indices of the fuzzy graph to the spherical fuzzy Zagreb indices of the spherical fuzzy graph (SFG). The spherical fuzzy Zagreb matrix of SFG and Zagreb energy of SFG are defined with examples. Additionally, we develop several lower and upper bounds of the spherical Zagreb energy of SFG. In addition, we present an application of SFG by computing its Zagreb energy in the decision-making problem of choosing the best location for business purposes.
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