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The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs.

Regular and Intra-Regular Semigroups in Terms of m-Polar Fuzzy Environment