Semigroups characterized by (∈,∈∨qk)-fuzzy ideals

2013

Generalizing the notions of -fuzzy left (right) ideal, -fuzzy quasi-ideal, and -fuzzy bi-ideal, the notions of -fuzzy left (right) ideal, -fuzzy quasi-ideal and -fuzzy bi-ideal of semigroups are defined. Regular, intra regular and semisimple semigroups are characterized by the properties of these fuzzy ideals.

2017

—The aims of this paper are to characterize fuzzy subsemigroups, fuzzy generalized bi-ideals, fuzzy bi-ideals and fuzzy quasi-ideals of semigroups. We de ne certain subsets of semigroups S, [0, 1] and S × [0, 1]. The relationships between sets of fuzzy points and the certain subsets of the semigroup S × [0, 1] are discussed. In the main results, characterizations of fuzzy subsemigroups, fuzzy generalized bi-ideals, fuzzy biideals and fuzzy quasi-ideals of semigroups are investigated by using the certain subsets of semigroups S, [0, 1] and S× [0, 1]. Index Terms—fuzzy subsemigroups, fuzzy generalized biideals, fuzzy bi-ideals, fuzzy quasi-ideals, semigroups.

Applied Mathematical Sciences, 2016

The notion of (α, β)-fuzzy left (right, bi-) ideals in semigroups is introduced, and related properties are investigated. Characterizations of (∈, ∈ ∨ q δ 0)-fuzzy left (right, bi-) ideals are provided.

ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 2017

In this article we define the notion of (∈, ∈ ∨ (k * , q k))fuzzy left (right) ideals, (∈, ∈ ∨ (k * , q k))-fuzzy (generalized) bi-ideals, (∈, ∈ ∨ (k * , q k))-fuzzy interior ideals and (∈, ∈ ∨ (k * , q k))-fuzzy quasiideals in semigroups. Finally we characterized regular semigroup by the properties of these ideals.

Journal of Mathematics, 2013

We have characterized right weakly regular semigroups by the properties of their(∈,∈∨qk)-fuzzy ideals.

Computers & Mathematics with Applications, 2010

Using the ideas of belonging and quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (α, β)-fuzzy ideals and (α, β)-fuzzy generalized bi-ideals, which are generalization of fuzzy ideals and fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. We also define the lower and upper parts of fuzzy subsets of a semigroup. Characterizations of regular semigroups by the properties of the lower part of (∈, ∈ ∨q)-fuzzy left ideals, (∈, ∈ ∨q)-fuzzy quasi-ideals and (∈, ∈ ∨q)-fuzzy generalized bi-ideals are given.

Thai Journal of Mathematics, 2017

The notion of (a, b)-fuzzy bi-ideals in semigroups is introduced, and related properties are investigated. Characterizations of (in, inVqd0)-generalized fuzzy bi-ideals are provided.

Fuzzy Sets and Systems, 1997

The purpose of this paper is to introduce some basic concepts of fuzzy algebra such as fuzzy (left, right) ideal and fuzzy bi-ideal in fuzzy semigroup, through the new approach of fuzzy space and fuzzy group introduced by Dib (1994). Our notion of fuzzy ideal and fuzzy bi-ideal includes the (classical) concepts of fuzzy ideal and fuzzy bi-ideal of ordinary semigroup. Many counterexamples are also given.

The Korean Journal of Mathematics, 2020

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irre-ducible fuzyy generalized m-bi-ideals.

Journal of Mathematics Research, 2010

In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right) quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals.