Clustering algorithm with strength of connectedness for $ m $-polar fuzzy network models

Abstract

<abstract><p>In this research study, we first define the strong degree of a vertex in an $ m $-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete $ m $-polar fuzzy graphs. Further, we introduce the concept of $ m $-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete $ m $-polar fuzzy graphs. We discuss connectivity parameters in $ m $-polar fuzzy graphs with precise examples, and we investigate the $ m $-polar fuzzy analogue of Whitney's theorem. Furthermore, we present a clustering method for vertices in an $ m $-polar fuzzy graph based on the strength of connectedness between pairs of vertices. In order to formulate this method, we introduce terminologies such as $ \epsilon_A $-reachable vertices in $ m $-polar fuzzy graphs, $ \epsilon_A $-connected $ m $-polar fuzzy graphs, or $ \epsilon_A $-connected $ m $-polar fuzzy subgraphs (in case the $ m $-polar fuzzy graph itself is not $ \epsilon_A $-connected). Moreover, we discuss an application for clustering different companies in consideration of their multi-polar uncertain information. We then provide an algorithm to clearly understand the clustering methodology that we use in our application. Finally, we present a comparative analysis of our research work with existing techniques to prove its applicability and effectiveness.</p></abstract>

Fuzzy clustering algorithm for university students' psychological fitness and performance detection

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Directed rough fuzzy graph with application to trade networking

“…Many researchers have addressed decision-making based on rough sets or their hybrid models in their research articles (Akram et al. 2022 ; Ma et al. 2017 ; Riaz et al.…”

“…Rough set has proven to be very useful in decision-making problems. Many researchers have addressed decision-making based on rough sets or their hybrid models in their research articles (Akram et al 2022;Ma et al 2017;Riaz et al 2021). Chen et al (2008) and Chen and Zhong (2011) worked on granular structures and a hypergraph model for granular computing in graphs.…”

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