On m-Polar Interval-valued Fuzzy Graph and its Application

Abstract

In this paper, the concept of the -polar fuzzy graph (-PFG) and interval-valued fuzzy graph (IVFG) is integrated and introduced an unprecedented kind of fuzzy graph designated as -polar interval-valued fuzzy graph (-PIVFG). Complement of the -PIVFG is defined and the failure of this definition in some cases are highlighted. Various examples are cited and then redefined the notation of complement such that it applies to all -PIVFGs. The other algebraic properties such as isomorphism, weak isomorphism, co-weak isomorphism of the -PIVFG are investigated. Moreover, some basic results on the isomorphic property of -PIVFG are proved. Finally, an application of -PIVFG is explored. Abbreviations: The following abbreviations are employed in this study: FS: Fuzzy set; FG: Fuzzy graph; IVFS: Interval-valued fuzzy sets; IVFG: Interval-valued fuzzy graph; -PFS: -polar fuzzy sets; -PFG: -polar fuzzy graph; -PIVFS: -polar interval-valued fuzzy sets; -PIVFG: -polar interval-valued fuzzy graph.