An efficient approach to study multi-polar fuzzy ideals of semirings.

ABSTRACT

The multi polar fuzzy (m-PF) set has an extensive range of implementations in real world problems related to the multi-polar information, multi-index and multi-attributes data. This paper introduces innovative extensions to algebraic structures. We present the definitions and some important results of m-polar fuzzy subsemirings (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings. The main contributions of the paper include the derivation and proof of key theorems that shed light on the algebraic interplay and computational aspects of m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings along with examples. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semirings by the properties of these ideals.