(∈, ∈ Vq)-Fuzzy Ideals in Semirings

Abstract

AbstractFollowing Bhakat and Das [21], Dudek et. al. [47], Ma and Zhan [106] defined (∈, ∈ Vq)-fuzzy ideals in semirings. In this chapter we have studied properties of these fuzzy ideals. In Section 1, we look at (α,β)-fuzzy ideals, and show that a fuzzy left (right) ideal of a semiring is an (∈, ∈)-fuzzy left (right) ideal. Section 2 provides a characterization of (∈, ∈ Vq)-fuzzy left (right) ideals, quasi and bi-ideals of semirings. Section 3 presents characterizations of regular semirings involving these ideals and Section 4 contains characterizations of regular and intra regular semirings by these ideals. Section 5 presents a study of (∈, ∈ Vq)-fuzzy k-ideals, k-quasi-ideals and k-bi-ideals of semirings. A study of k-regular and k-intra regular semirings in this context is separately made in Sections 6 and 7.Throughout this chapter R is a semiring with zero element.KeywordsComputational IntelligencePositive Real NumberNonempty SubsetLeft IdealFuzzy SubsetThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.