A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

Abstract

This paper provides a generalized form of ideals, that is, h-ideals of hemirings with the combination of a bipolar fuzzy set (BFS). The BFS is an extension of the fuzzy set (FS), which deals with complex and vague problems in both positive and negative aspects. The basic purpose of this paper is to introduce the idea of$\left(\alpha ,\beta \right)-$bipolar fuzzy h-subhemirings (h-BFSHs),$\left(\alpha ,\beta \right)-$bipolar fuzzy h-ideals (h-BFIs), and$\left(\alpha ,\beta \right)-$bipolar fuzzy h-bi-ideals (h-BFbIs) in hemirings by applying the definitions of belongingness$\left(\in \right)$and quasicoincidence$\left(q\right)$of the bipolar fuzzy point. We will also focus on upper and lower parts of the h-product of bipolar fuzzy subsets (BFSSs) of hemirings. In the end, we have characterized the h-hemiregular and h-intrahemiregular hemirings in terms of the$\left(\in ,\in \vee q\right)-$h-BFIs and$\left(\in ,\in \vee q\right)-$h-BFbIs.