On fuzzy KS-semigroups

Computers & Mathematics with Applications, 2010

k)-fuzzy ideal (∈, ∈ ∨q k)-fuzzy quasi-ideal (∈, ∈ ∨q k)-fuzzy bi-ideal a b s t r a c t Generalizing the notions of (∈, ∈ ∨q)-fuzzy ideal, (∈, ∈ ∨q)-fuzzy quasi-ideal and (∈, ∈ ∨q)-fuzzy bi-ideal, the concepts of (∈, ∈ ∨q k)-fuzzy ideal, (∈, ∈ ∨q k)-fuzzy quasiideal and (∈, ∈ ∨q k)-fuzzy bi-ideal are defined. Different classes of semigroups are characterized by the properties of these fuzzy ideals.

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.

In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory , the use of fuzzified algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (∈, ∈ ∨q k)-fuzzy subsystems of ordered semigroups namely (∈, ∈ ∨q k)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (∈, ∈ ∨q k)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (∈, ∈ ∨q k)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

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.

2012

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy left (right) ideal of an ordered semigroup S and introduce a new sort of fuzzy left (right) ideals called (∈, ∈ ∨q k)-fuzzy left (right) ideals, where k ∈ [0, 1). In particular, we describe the relationships among ordinary fuzzy ideals and (∈, ∈ ∨q k)fuzzy ideals of an ordered semigroup S. Finally, we characterize regular ordered semigroups in terms of (∈, ∈ ∨q k)-fuzzy left (resp. right) 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.

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.

2017

The inception of the notion of a fuzzy set, introduced by Zadeh (1965), laid the foundations and frame works as well as gave birth to great researches. This notion has been the subject of great attention to many researchers and consequently a series of interesting results have been published. In fact, the concept of ordered semigroups and Γsemigroups is a generalization of semigroups. Also the ordered Γsemigroup is a generalization of Γ-semigroups and this concept was introduced by M.K. Sen (1981). The notion of a bi-ideal was first introduced by Good and Hughes (1952). Kazancı and Yamak (2008) introduced the concept of a generalized fuzzy bi-ideal in semigroups

Journal of Advanced Mathematics and Applications, 2015

An ordered semigroup (algebraic structure) is a semigroup together with a partial order that is compatible with the semigroup operation. In many applied disciplines like computer science, coding theory, sequential machines and formal languages, the use of fuzzified algebraic structures especially ordered semigroups play a remarkable role. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we introduce the concepts of ()-fuzzy biideals and ()-fuzzy bi-ideals of ordered semigroups, where ∈ ∈ q ∈ ∧q ∈ ∨q ∈ ∈ q ∈ ∧ q ∈ ∨ q , =∈ ∧q and = ∈ ∧ q , and some related properties are investigated. The important milestone of this paper is, to link ordinary bi-ideals and fuzzy bi-ideals of types (∈ ∈ ∨q) and (∈ ∈ ∨ q) using level subset U r. Special attention is paid to (∈ ∈ ∨q)fuzzy bi-ideals and (∈ ∈ ∨ q)-fuzzy bi-ideals.

Journal of Intelligent & Fuzzy Systems, 2018

In this paper, applying the theory of L-fuzzy sets, we introduce the concept of an L-fuzzy ideal (L-fuzzy k-ideal) of an m-ary semigroup. Some properties of them are investigated and some structural theorems for L-fuzzy ideals (L-fuzzy k-ideals) of m-ary semigroups are proved. In this direction the concept of image and preimage of an L-fuzzy set under m-ary semigroup homomorphism are discussed. Also, the notions of normal L-fuzzy ideal (L-fuzzy k-ideal) and maximal L-fuzzy ideal (L-fuzzy k-ideal) of an m-ary semigroup are introduced and some properties of them are studied. Further, we introduce the notion of L-fuzzy congruence on an m-ary semigroup and make a study of L-fuzzy quotient m-ary semigroup using an L-fuzzy congruence, an L-fuzzy quotient m-ary semigroup induced by L-fuzzy ideals. We also investigate some properties of homomorphisms between them.