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A Decision-Making Analysis with Generalized m-Polar Fuzzy Graphs
Saba Siddique, Uzma Ahmad and Muhammad Akram

The m-polar fuzzy graph model is the backbone of many realistic uncertain systems where the information depends on multi-attribute or multi-object uncertainty rather than a single-one. However, due to the particular restriction on edges, these graph models are reserved to represent for some specific systems. A generalized m-polar fuzzy graph model is an appropriate tool to avoid such restriction. It is an extended approach and gives more flexibility as compared to an m-polar fuzzy graph model. In this study, we introduce the notion of generalized m-polar fuzzy graph of type-I and describe its matrix representation. We also present some useful properties, including regularity and completeness of generalized m-polar fuzzy graphs of type-I. In addition, we demonstrate these properties by certain examples and illustrate some related results. Furthermore, we display an application of generalized m-polar fuzzy graphs of type-I in decision-making, that is, selection of best candidate for the post of administrator in an organization. Moreover, we design an algorithm for describing the general procedure of our application. Finally, we conduct a comparative analysis to specify the importance of our introduced model with the existing models.

Keywords: Generalized m-polar fuzzy graphs of type-I, regular graphs, effective graphs, application, comparative analysis

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