Author
T. K. Dutta
Bio: T. K. Dutta is an academic researcher from University of Calcutta. The author has contributed to research in topics: Fuzzy logic & Fuzzy classification. The author has an hindex of 4, co-authored 7 publications receiving 95 citations.
Papers
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TL;DR: In this paper, the notion of operator semirings of a Γ-semiring was introduced to study Γ -semirings. And it was shown that the lattices of all left (right) ideals (two-sided ideals) of the Γsemiring and its right (respectively left) operator semiring are isomorphic.
Abstract: In this paper we introduce the notion of operator semirings of a Γ-semiring to study Γ-semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a Γ-semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various Γ-semirings.
39 citations
01 Jan 2009
TL;DR: The main purpose of as discussed by the authors is to explore new relationships between a Γ-semigroup and its operator semigroups in terms of fuzzy ideals so as to apply them, together with the already obtained such relationships, in the study of fuzzy ideal extension of Γ -semigroups.
Abstract: The main purpose of this paper is to explore new relationships between a Γ-semigroup and its operator semigroups in terms of fuzzy ideals so as to apply them, together with the already obtained such relationships, in the study of fuzzy ideal extension of Γ-semigroups.
27 citations
01 Jan 2009
TL;DR: In this article, the concept of the extensions of fuzzy ideals in a semigroup has been extended to a Γ-semigroup and the results of fuzzy ideal extension in terms of prime ideal extension have been obtained.
Abstract: In this paper the concept of the extensions of fuzzy ideals in a semigroup has been extended to a Γ-semigroup. Among other results characterization of prime ideals in a Γ-semigroup in terms of fuzzy ideal extension has been obtained. Mathematics Subject Classification: 20M12, 03F55, 08A72
19 citations
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01 Jan 2011
TL;DR: Different types of operations on fuzzy ideals of −semirings are introduced and it is proved subsequently that these oprations give rise to different structures such as complete lattice, modular lattice on some restricted class of fuzzy ideal of − semirings.
Abstract: The purpose of this paper is to introduce different types of operations on fuzzy ideals of −semirings and to prove subsequently that these oprations give rise to different structures such as complete lattice, modular lattice on some restricted class of fuzzy ideals of −semirings. A characterization of a regular −semiring has also been obtained in terms of fuzzy subsets.
6 citations
TL;DR: In this paper, the authors studied Noetherian Γ-semirings and obtained Cohen's theorem for weak primary decomposition for a special class of Γ semirings.
Abstract: In this paper we study Noetherian Γ-semirings and obtain Cohen’s theorem for a special class of Γ-semirings Weak primary decomposition theorem for a particular type of Γ-semirings is also obtained
4 citations
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01 Jan 2005
TL;DR: In this paper, the notions of Jacobson radical of a semiring and semisimple semiring were introduced and characterized via operator semirings, and a number of characterizations of semimodule semiring was obtained.
Abstract: We introduce the notions of Jacobson radical of a semiring and semisimple semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10 characterizations. We obtain the relation between the Jacobson radical of a semiring S and that of the right operator semiring R of S, which we use to obtain characterizations of Jacobson radical of a semiring analogous to familiar results of the ring theory and semiring theory, (5). Then, with the help of the notion of subdirect sum of semiring, introduced at the outset in a similar way to that in ring, (6), and using the result that "a semiring S is semisimple if and only if its right operator semi- ring R is semisimple", a number of characterizations of semisimple semiring is obtained. For preliminaries of semirings, semirings, operator semirings of a semi- ring and rings we refer to (4), (9), (1), (6) and references therein. Throughout this paper a semiring is assumed to be with zero, the left unity, the right unity. It is also assumed that a S semimodule is additively cancellative.
38 citations
01 Jan 2009
TL;DR: The main purpose of as discussed by the authors is to explore new relationships between a Γ-semigroup and its operator semigroups in terms of fuzzy ideals so as to apply them, together with the already obtained such relationships, in the study of fuzzy ideal extension of Γ -semigroups.
Abstract: The main purpose of this paper is to explore new relationships between a Γ-semigroup and its operator semigroups in terms of fuzzy ideals so as to apply them, together with the already obtained such relationships, in the study of fuzzy ideal extension of Γ-semigroups.
27 citations
TL;DR: Fuzzify the notions of interior ideals and characteristic interior ideals of a @C-semigroup, and investigate some of their basic properties, resulting in a characterization of a simple @C -semigroup in terms of fuzzy interior ideals.
Abstract: In this paper, we fuzzify the notions of interior ideals and characteristic interior ideals of a @C-semigroup, and investigate some of their basic properties. Finally, a characterization of a simple @C-semigroup in terms of fuzzy interior ideals is obtained.
25 citations
01 Jan 2012
TL;DR: In this paper the notions of bipolar valued fuzzy subsemigroup,ipolar valued fuzzy bi-ideal, bipolar value fuzzy (1,2)- ideal and bipolar valued furry ideal in a -semigroup have been introduced and important characterizations are obtained.
Abstract: In this paper the notions of bipolar valued fuzzy subsemigroup, bipolar valued fuzzy bi-ideal, bipolar valued fuzzy (1,2)- ideal and bipolar valued fuzzy ideal in a Γ-semigroup have been introduced. Some important characterizations are also obtained.
23 citations
TL;DR: This paper continues the study on intuitionistic fuzzy sets in Γ-semihypergroups initiated recently by Ersoy and Davvaz and introduces and studies λ, μ-intuitionistic fuzzyΓ-hyperideals, a generalization of the notion of fuzzy sets.
Abstract: The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, using Atanassov idea, we continue the study on intuitionistic fuzzy sets in Γ-semihypergroups initiated recently by Ersoy and Davvaz [25]. We give some further properties of intuitionistic fuzzy Γ-hyperideals and intuitionistic fuzzy bi-Γ-hyperideals in a Γ-semihypergroup and use the intuitionistic fuzzy left, right, two-sided and bi-Γ-hyperideals to characterize some classes of Γ-semihypergroups. We introduce and study λ, μ-intuitionistic fuzzy Γ-hyperideals. We also introduce the notion of an intuitionistic fuzzy M resp. N-hypersystem of a Γ-semihypergroup and some properties of them are investigated.
22 citations