Author
Sujit Kumar Sardar
Other affiliations: University of Calcutta
Bio: Sujit Kumar Sardar is an academic researcher from Jadavpur University. The author has contributed to research in topics: Fuzzy logic & Fuzzy subalgebra. The author has an hindex of 6, co-authored 58 publications receiving 247 citations. Previous affiliations of Sujit Kumar Sardar include University of Calcutta.
Papers
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01 Jan 2009
TL;DR: In this article, the notion of fuzzy ideals of a regular Γ-semigroup has been introduced and some of their properties have been investigated, such as operator semigroups and fuzzy ideals.
Abstract: In this paper the notion of fuzzy ideals of a Γ-semigroup has been introduced and some of their properties have been investigated. Characterization of a regular Γ-semigroup in terms of fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between fuzzy ideals of a Γsemigroup and that of its operator semigroups. These results are then used to revisit some results of Γ-semigroups. Mathematics Subject Classification[2000]: 20M12, 03F55, 08A72
34 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 2009
TL;DR: The notion of fuzzy prime ideal in Γ-semigroups has been introduced and studied in this paper and the relationship between prime ideals of a Γsemigroup and that of its operator semigroups have been obtained.
Abstract: In this paper the notion of fuzzy prime ideal in Γ-semigroups has been introduced and studied. Relationship between prime ideals of a Γ-semigroup and that of its operator semigroups have been obtained which are used to revisit analogous results on ideals of Γ-semigroups and its operator semigroups.
24 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 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 Feb 2016
TL;DR: The notion of falling fuzzy interior ideals of a hemiring is introduced and some related properties are investigated, and some characterizations of quasi-hemiregular hemirings based on independent (perfect positive correlation) probability spaces are investigated.
Abstract: The notion of falling fuzzy $$h$$h-interior ideals of a hemiring is introduced and some related properties are investigated. A special attention is given to two kinds of certain and impossible probability spaces. Finally, we investigate some characterizations of $$h$$h-semisimple and $$h$$h-quasi-hemiregular hemirings based on independent (perfect positive correlation) probability spaces.
28 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
TL;DR: A study on bipolar fuzzy sets in Γ-semihypergroups, which defines bipolar fuzzy left (right, bi-, interior, (1,2)-)Γ-hyperideals and explores some related properties.
Abstract: The theory of bipolar fuzzy sets introduced by Lee [9] has been applied to many branches of mathematics. In this paper, we initiate a study on bipolar fuzzy sets in Γ-semihypergroups. We define bipolar fuzzy left (right, bi-, interior, (1,2)-) Γ-hyperideals and explore some related properties. We use these bipolar fuzzy Γ-hyperideals to characterize some classes of Γ-semihypergroups. We consider the Γ-semihypergroup $\underline{\mathcal{H}}$ of the bipolar fuzzy points of a Γ-semihypergroup H to discuss the relation between the bipolar fuzzy sub Γ-semihypergroup (left, right, bi-, interior, (1,2)-) Γ-hyperideal and the subsets of $\underline{\mathcal{H}}$ in a (regular) Γ-semihypergroup. In the end, we discuss in detail a number of results on homomorphic images and preimages of bipolar fuzzy Γ-hyperideals.
25 citations