A New Approach to Evaluate Regular Semirings in terms of Bipolar Fuzzy k‐Ideals Using k‐Products

Abstract

In this paper, we provide a generalized form of ideals that is k‐ideals of semirings with the combination of a bipolar fuzzy set (BFS). The BFS is a generalization of fuzzy set (FS) that deals with uncertain problems in both positive and negative aspects. The main theme of this paper is to present the idea of (α, β)‐bipolar fuzzy k‐subsemiring (k‐BFSS), (α, β)‐bipolar fuzzy k‐ideals (k‐BFIs), and (α, β)‐bipolar fuzzy k‐bi‐ideals (k‐BFbIs) in semirings by applying belongingness (∈) and quasi‐coincidence (q) of the bipolar fuzzy (BF) point. After that, upper and lower parts of k‐product of BF subsets of semirings are introduced. Lastly, the notions of k‐regular and k‐intraregular semirings in terms of (∈, ∈∨q)‐k–BFIs and (∈, ∈∨q)‐k–BFbIs are characterized.