arXiv subjects
Publications and source records attributed to Samit Kumar Majumder.
In this paper, using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (epsilon, epsilon join q)- fuzzy subsemigroup and (epsilon, epsilon join q)- fuzzy bi-ideal in a gamma-semigroup have been introduced and some related properties have been investigated.
The purpose of this paper is to investigate some properties of fuzzy ideals and fuzzy bi-ideals in gamma-semigroups and to introduce the notion of fuzzy quasi ideals in gamma-semigroups. Here we also characterize a regular gamma-semigroup in terms of fuzzy quasi ideals.
The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. S.K Sardar and S.K. Majumder unified the idea of fuzzy translation and fuzzy multiplication of Vasantha Kandasamy to introduce the concept of fuzzy magnified translation in groups and semigroups. The purpose of this paper is to intuitionistically fuzzify(by using Atanassov's idea) the concept of fuzzy magnified translation in semigroups. Here among other results we obtain some characterization theorems of regular, intra-regular, left(right) regular semigroups in terms of intuitionistic fuzzy magnified translation.
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 gamma semigroups in order to obtain some characterization theorems. We also introduce the notion of Atanassov's intuitionistic fuzzy ideal extension in a gamma semigroup and investigate some of their important properties. A regular gamma semigroup has been characterized in terms of Atanasov's intutionistic fuzzy ideal. Characterization of prime ideal of a gamma semigroup has also been obtained in terms of Atanassov's intutionistic fuzzy ideal extension.
In this paper some fundamental relationships of a gamma semigroup and its operator semigroups in terms of intuitionistic fuzzy subsets, intuitionistic fuzzy ideals, intuitionistic fuzzy prime(semiprime) ideals, intuitionistic fuzzy ideal extensions are obtained. These are then used to obtain some important characterization theorems of gamma semigroups in terms of intuitionistic fuzzy subsets so as to highlight the role of operator semigroups in the study of gamma semigroups in terms of intuitionistic fuzzy subsets.
In this paper the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.
In this paper the concept of Q-fuzzification of ideals of gamma-semigroups has been introduced and some important properties have been investigated. A characterization of regular gamma-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a gamma-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a gamma-semigroup and that of its operator semigroups.
In this paper the concept of fuzzy characteristic interior ideals in partially ordered gamma-semigroups(Po-gamma-semigroups) has been introduced. It is observed that it satisfies level subset criterion and characteristic function criterion.
The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S: