36 research outputs found
Characterizations of hemirings by their -ideals
In this paper we characterize hemirings in which all -ideals or all fuzzy
-ideals are idempotent. It is proved, among other results, that every
-ideal of a hemiring is idempotent if and only if the lattice of fuzzy
-ideals of is distributive under the sum and -intrinsic product of
fuzzy -ideals or, equivalently, if and only if each fuzzy -ideal of
is intersection of those prime fuzzy -ideals of which contain it. We
also define two types of prime fuzzy -ideals of and prove that, a
non-constant -ideal of is prime in the second sense if and only if each
of its proper level set is a prime -ideal of
Characterizations of Hemirings Based on Probability Spaces
The notion of falling fuzzy h-ideals of a hemiring is introduced on the basis of the theory of falling shadows and fuzzy sets. Then the relations between fuzzy h-ideals and falling fuzzy h-ideals are described. In particular, by means of falling fuzzy h-ideals, the charac-terizations of h-hemiregular hemirings are investigated based on independent (prefect positive correlation) probability spaces
Intuitionistic fuzzy k-ideals of right k-weakly regular hemirings
In this work, we will examine the concept of intuitionistic fuzzy k-ideals in the context of right k-weakly regular hemirings. We will investigate the properties of these ideals and how they relate to other concepts such as fuzzy prime k-ideals, intuitionistic fuzzy prime k-ideals, intuitionistic fuzzy right pure k-ideals, and purely prime intuitionistic fuzzy k-ideals in hemirings. We will also explore how the regularity of a k-weakly regular hemiring can be characterized through its intuitionistic fuzzy k-ideals
A new generalization of fuzzy ideals in LA-semigroups
Abstract. In this article, the concept of (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy LAsubsemigroups, (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy left(right) ideals, (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy generalized bi-ideals and (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy bi-ideals of an LA-semigroup are introduced. The given concept is a generalization of (β, β β¨ q)-fuzzy LA-subsemigroups, (β, β β¨ q)-fuzzy left(right) ideals, (β, β β¨ q)-fuzzy generalized bi-ideals and (β, β β¨ q)-fuzzy bi-ideals of an LA-semigroup. We also give some examples of (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy LA-subsemigroups ( left, right, generalized bi-and bi) ideals of an LA-semigroup. We prove some fundamental results of these ideals. We characterize (β Ξ³ , βΞ³ β¨ q Ξ΄ )-fuzzy left(right) ideals, (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy generalized bi-ideals and (βΞ³, βΞ³ β¨ q Ξ΄ )-fuzzy bi-ideals of an LA-semigroup by the properties of level sets
On properties of generalized bipolar fuzzy semigroups
In this paper, we introduce a generalization of a bipolar fuzzy subsemigroup, namely a (1, 2; 1, 2)-bipolar fuzzy
subsemigroup. The notions of (1, 2; 1, 2)-bipolar fuzzy left (right, bi-) ideals are discussed. Some necessary and sufficient
conditions of (1, 2; 1, 2)-bipolar fuzzy left (right, bi-) ideals are obtained. Furthermore, any regular semigroup is
characterized in terms of generalized bipolar fuzzy semigroup
Regular ag-groupoids characterized by (β, β β¨ q k)-fuzzy ideals
In this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in AG -groupoids. Generalizing the concepts of (β, β β¨q) -fuzzy bi-ideals (interior ideal), we define (β, β β¨ q k) -fuzzy bi-ideals, (β, β β¨ q k )-fuzzy left (right)-ideals and ( , ) k ? ? ?q -fuzzy interior ideals in AG -groupoids and discuss some fundamental aspects of these ideals in AG -groupoids. We further define ( β, β β¨ q k) -fuzzy bi-ideals and (β, β β¨ q k)-fuzzy interior ideals and give some of their basic properties in AG -groupoids. In the last section, we define lower/upper parts of (β, β β¨ q k ) -fuzzy left (resp. right) ideals and investigate some characterizations of regular and intera-regular AG -groupoids in terms of the lower parts of ( β, β β¨ q k ) -fuzzy left (resp. right) ideals and ( β, β β¨ q k )-fuzzy bi-ideal of AG -groupoids