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Intuitionistic Fuzzy Points in Semigroups  [PDF]
Sujit Kumar Sardar,Manasi Mandal,Samit Kumar Majumder
Mathematics , 2011,
Abstract: 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:
Intuitionistic Fuzzy Ideal Extensions of Γ-Semigroups  [PDF]
Nayyar Mehmood,Imran Haider Qureshi
Mathematics , 2010,
Abstract: In this paper the concept of the extensions of intuitionistic fuzzy ideals in a semigroup has been extended to a {\Gamma}-Semigroups. Among other results characterization of prime ideals in a {\Gamma}-Semigroups in terms of intuitionistic fuzzy ideal extension has been obtained.
On Intuitionistic Fuzzy Magnified Translation in Semigroups  [PDF]
Sujit Kumar Sardar,Manasi Mandal,Samit Kumar Majumder
Mathematics , 2011,
Abstract: 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.
Quasicoincidence for intuitionistic fuzzy points
Francisco Gallego Lupiá ez
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.1539
Abstract: The introduction of intuitionistic fuzzy sets is due to K. T. Atanassov, who also proposed some problems about this subject. D. Çoker defined the intuitionistic fuzzy topological spaces and, with some coworkers, studied these spaces. In this paper, we define and study the notion of quasicoincidence for intuitionistic fuzzy points and obtain a characterization of continuity for maps between intuitionistic fuzzy topological spaces
Study of Gamma Semigroups via its Operator Semigroups in terms of Atanassov's Intuitionistic Fuzzy Ideals  [PDF]
Sujit Kumar Sardar,Samit Kumar Majumder,Manasi Mandal
Mathematics , 2011,
Abstract: 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.
Atanassov's Intuitionistic Fuzzy Ideals of Gamma Semigroups  [PDF]
Sujit Kumar Sardar,Samit Kumar Majumder,Manasi Mandal
Mathematics , 2011,
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 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.
Intuitionistic fuzzy interior ideals of semigroups
Kyung Ho Kim,Young Bae Jun
International Journal of Mathematics and Mathematical Sciences , 2001, DOI: 10.1155/s0161171201010778
Abstract: We consider the intuitionistic fuzzification of the concept of interior ideals in a semigroup S, and investigate some properties of such ideals. For any homomorphism f from a semigroup S to a semigroup T, if B=(μB,γB) is an intuitionistic fuzzy interior ideal of T, then the preimage f−1(B)=(f−1(μB),f−1(γB)) of B under f is an intuitionistic fuzzy interior ideal of S.
On fuzzy points in semigroups
Kyung Ho Kim
International Journal of Mathematics and Mathematical Sciences , 2001, DOI: 10.1155/s0161171201006299
Abstract: We consider the semigroup S¯ of the fuzzy points of a semigroup S, and discuss the relation between the fuzzy interior ideals and the subsets of S¯ in an (intra-regular) semigroup S.
Characterizing Fuzzy Sets in Ordered $Gamma$-Semigroups  [cached]
Aiyared Iampan
Journal of Mathematics Research , 2010, DOI: 10.5539/jmr.v2n4p52
Abstract: The motivation mainly comes from the fuzzification of sets that are of importance and interest in ordered semigroups, ordered ternary semigroups and ogs s. We can see that gs s are a generalization of semigroups and ternary semigroups. In this paper, we characterize the relationship between the foi s (fof s) and the chm s of foi s (fof s) in ogs s analogous to the characterizations of fuzzy ideals and fuzzy filter in ordered ternary semigroups considered by Chinram and Saelee (Chinram, R. & Saelee, S., 2010).
Characterizing semigroups by Q-fuzzy ideals  [PDF]
Caixia Li,Zhenji Tian
International Mathematical Forum , 2013,
Abstract: In this paper, we introduce the concept of Q-fuzzy left [right, twosided]ideal in semigroups. Moreover, the operations with Q-fuzzy setsand its related properties are discussed. Especially, we investigate therelationship between Q-fuzzy point and Q-fuzzy left [right] ideal. Finally,some theorems are given to characterize intra-regular semigroupsin terms of fuzzy semiprime Q-fuzzy [left, right] ideals.
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