Fuzzy h-ideals of hemirings

Abstract

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset ζ of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if ζ is two-valued, ζ(0) = 1, and the set of all x in S such that ζ(x) = 1 is a prime (left) right h-ideal of S. Finally, the similar properties for maximal fuzzy left (right) h-ideals of hemirings are considered.

Soft Hemirings Related to Fuzzy Set Theory

“…The notion of h-hemiregularity of a hemiring was first introduced by Zhan et al in [32]. In this section, we investigate the characterizations of h-hemiregular hemirings by soft set theory.…”

“…Consequently some more restricted concepts of ideals such as k-ideals [10] and h-ideals [11] have been introduced in the study of the semiring theory. Some researchers have investigated some important results of semirings, the notions of fuzzy semirings, fuzzy (prime) ideals, fuzzy h-ideals and obtained many good results (see [13,18,26,30,31,32,34]). Feng et.al [8] have started to investigate the structure of soft semirings.…”

Fuzzy ideals of ordered semigroups with fuzzy orderings

“…Particularly, it was pointed out in the same paper that .2; 2 _q/-fuzzy subgroup is an important and useful generalization of Rosenfeld's fuzzy subgroup. After that, these generalizations have been extended to other algebraic structures by many researchers, for example, Davvaz [4], Jun and Song [5], Kazancı and Yamak [6], Khan and Shabir [7], Yin et al [8], Zhan and Yin [9], Davvaz and Khan [10], etc. As a generalization of the quasi-coincident relation .q/ of a fuzzy point with a fuzzy subset, Jun [11] defined .2; 2 _q k /-fuzzy subalgebras in BCK/BCIalgebras.…”

CHARACTERIZATIONS OF HEMIRINGS BY ∊,∊∨q)-FUZZY IDEALS

“…Fuzzy kideals in semirings are studied in [11] and fuzzy h-ideals are studied in [10,17,20,25,26,28,30].…”