A realization of intuitionistic fuzzy ideals of semirings

Journal of Physics: Conference Series, 2019

The aim of this paper is to introduce the notion of intuitionistic fuzzy (1,2)-ideals in semigroups and to investigate some of their properties. The characterizations of intuitionistic fuzzy (1,2)-ideals in semigroups are provided. It is shows that the intersection of two intuitionistic fuzzy (1,2)-ideals of semigroups is also an intuitionistic fuzzy (1,2)-ideal.

International Journal of Fuzzy Logic and Intelligent Systems, 2009

We introduce the concepts of intuitionistic fuzzy k-ideals and intuitionistic fuzzy prime k-ideals of a semiring. And we investigate some properties of them.

Soft Computing, 2008

We introduce the notion of intuitionistic fuzzy left k-ideals of semirings and investigate their properties and connections with left k-ideals of the corresponding semirings. Next we give some important characterizations of intuitionistic fuzzy left k-ideals of different type and describe various methods of constructions of such intuitionistic fuzzy sets. Finally, we propose some natural classification of intuitionistic fuzzy left k-ideals.

In this paper, we made an attempt to study the algebraic nature of intuitionistic fuzzy subsemiring of a semiring.

2012

In this paper, using t-norm ∆ and s-norm∇ we introduce the notion of generalized intuitionistic fuzzy bi-ideal, generalized intuitionistic fuzzy generalized bi-ideal and generalized intuitionistic fuzzy (1,2) ideal of a semigroup. We characterize different classes of semigroups by the properties of these fuzzy ideals.

Afrika Matematika, 2019

In 1995, Murali (Southeast Asian Bull Math 19:49-54, 1995) introduced the concept ofsemiring. In this study we will discuss the intuitionistic Q-fuzzy k-ideal and intuitionistic Q-k-fuzzy ideal notion in-semiring and study the properties related to them. Finally we have the explained the intuitionistic Q-fuzzy k-ideals and intuitionistic k-Q-fuzzy ideals under homomorphism and established some results on these.

2019

In this article, we introduce the notion of (∈,∈ ∨qk)-intuitionistic fuzzy subsemigroup, (∈,∈ ∨qk)-intuitionistic fuzzy left (resp. right) ideals, (∈,∈ ∨qk)-intuitionistic fuzzy bi-ideals and (∈,∈ ∨qk)-intuitionistic fuzzy (1, 2)-ideals and study some of its properties. We study the related properties of the (∈,∈ ∨qk)-intuitionistic fuzzy bi-ideals, (1, 2)-ideals and in particular, an (∈,∈ ∨qk)-fuzzy bi-ideals and (1, 2)-ideals in semigroups will be investigated.

2015

The importance of semigroups and their fuzzy subsystems is evident from their applications and significant role in several applied dis-ciplines like computer sciences, control engineering, error-correcting codes and fuzzy automata theory. In this paper, we give generalizations of in-tuitionistic fuzzy interior ideals of semigroups and introduced the notions of intuitionistic fuzzy interior ideals of type (V qk) and of semi-groups. The important mile stone of the present paper is to link ordinary intuitionistic fuzzy interior ideals, intuitionistic fuzzy interior ideals and (V qk)-intuitionistic fuzzy interior ideals. Moreover semigroups are characterized by the properties of these notions.

2011

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the notion of Atanassov’s intuitionistic fuzzy ideal extension in a Γ-semigroup and investigate some of their important properties. A regular Γ-semigroup has been characterized in terms of Atanasov’s intutionistic fuzzy ideal. Characterization of prime ideal of a Γ-semigroup has also been obtained in terms of Atanassov’s intutionistic fuzzy ideal extension.

Annals of Pure and Applied Mathematics, 2017

A Q-fuzzy set is a mapping from [0,1] X Q × → where X is the universe of discourse and Q is a non-empty set. Some works has been emanated for this Q-fuzzy set. In all the above work the set 'Q' is treated as a non-empty set without any algebraic structure. This article presents an algebraic structure for Q-fuzzy set over a semiring named as 1 Q-fuzzy set and provide some properties and results.