Author: Takaaki Fujita
DOI Link: https://doi.org/10.70798/Bijmrd/04080003
Abstract: Graph-based models provide a fundamental mathematical framework for representing relational systems in terms of vertices and their connections. Fuzzy sets extend classical set theory by assigning each element a membership degree in the interval [0,1], thereby allowing partial membership rather than restricting membership to binary values. Through the use of HyperStructures [17], Fuzzy Sets have been generalized to HyperFuzzy Sets [18–20]. Furthermore, the HyperFuzzy Set framework has been extended to graph-theoretic settings, leading to the development of HyperFuzzy Graphs [39–41].Motivated by these developments, this paper investigates tripolar extensions of the hyperfuzzy framework. In particular, we study Tripolar HyperFuzzy Sets and Tripolar HyperFuzzy Graphs, which integrate the three-pole representation of tripolar fuzzy models with the set-valued membership structure underlying HyperFuzzy Sets and HyperFuzzy Graphs
Keywords: HyperFuzzy Set, HyperFuzzy Graph, Tripolar Fuzzy Set.
Page No: 16-25