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Fuzzy Sets and Systems, 2016
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Budimirovic, Branka +3 more
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Budimirovic, Branka +3 more
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Free fuzzy groups and fuzzy group presentations
Fuzzy Sets and Systems, 1992Free fuzzy semigroups were considered by \textit{G. Gerla} [Ric. Mat. 33, 53-62 (1984; Zbl 0582.20037)]. This paper introduces a definition of free fuzzy groups and brings some analogs to the combinatorial group theory. A new notion of quotients of fuzzy groups is also introduced [cf. \textit{I. J. Kumar}, \textit{P. K. Saxena} and \textit{P.
Garzon, Max, Muganda, Godfrey C.
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Fuzzy Sets and Systems, 1991
The concept of \(L\)-fuzzy topological groups is introduced as follows: Let \(X\) be a group and \(J\) be an \(L\)-fuzzy topology on \(X\). The pair \((X,J)\) is said to be an \(L\)-fuzzy topological group, if and only if the following conditions are satisfied: (a) The mapping \(g: (x,y)\to xy\) of the product \(L\)-fuzzy topological space \((X,J ...
Yu, Chunhai, Ma, Jiliang
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The concept of \(L\)-fuzzy topological groups is introduced as follows: Let \(X\) be a group and \(J\) be an \(L\)-fuzzy topology on \(X\). The pair \((X,J)\) is said to be an \(L\)-fuzzy topological group, if and only if the following conditions are satisfied: (a) The mapping \(g: (x,y)\to xy\) of the product \(L\)-fuzzy topological space \((X,J ...
Yu, Chunhai, Ma, Jiliang
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Fuzzy Sets and Systems, 2010
\textit{D. H. Foster} [J. Math. Anal. Appl. 67, 549--564 (1979; Zbl 0409.22001)] first introduced the notion of fuzzy topological groups. In the present paper, the concept of \(I\)-fuzzy topological groups is introduced and fundamental framework of \(I\)-fuzzy topological groups is established.
Yan, Cong-Hua, Guo, Sheng-Zhang
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\textit{D. H. Foster} [J. Math. Anal. Appl. 67, 549--564 (1979; Zbl 0409.22001)] first introduced the notion of fuzzy topological groups. In the present paper, the concept of \(I\)-fuzzy topological groups is introduced and fundamental framework of \(I\)-fuzzy topological groups is established.
Yan, Cong-Hua, Guo, Sheng-Zhang
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Fuzzy groups: Some group-theoretic analogs
Information Sciences, 1986The standard results of group theory are formulated and proved with fuzzy groups, fuzzy cosets, fuzzy normal groups and fuzzy index. It is a continuation of a previous paper on fuzzy groups [the authors, ibid. 34, 225-239 (1984; Zbl 0568.20002)].
Mukherjee, N. P., Bhattacharya, Prabir
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Fuzzy Sets and Systems, 1999
The fuzzy subhypergroups of a hypergroup and the fuzzy \(H_v\)-group of an \(H_v\)-group are defined and studied in this paper. The most interesting result is the main theorem concerning the fundamental group of the underlying \(H_v\)-group. This result proves, once more, how interesting the fundamental relations in the study of hyperstructures are.
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The fuzzy subhypergroups of a hypergroup and the fuzzy \(H_v\)-group of an \(H_v\)-group are defined and studied in this paper. The most interesting result is the main theorem concerning the fundamental group of the underlying \(H_v\)-group. This result proves, once more, how interesting the fundamental relations in the study of hyperstructures are.
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Fuzzy relations and fuzzy groups
Information Sciences, 1985The main result: Given a group \(G\) and a fuzzy set \(A\) on \(G\), \(A\) is a fuzzy group on \(G\) iff \(A\times A\) is a fuzzy group on \(G\times G\). A more general product of fuzzy groups was considered by \textit{H. Sherwood} [Fuzzy Sets Syst. 11, 79--89 (1983; Zbl 0529.20021)].
Bhattacharya, Prabir, Mukherjee, N. P.
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Fuzzy groups and group homomorphisms
Fuzzy Sets and Systems, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sebastian, Souriar, Sundar, S. Babu
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Fuzzy Sets and Systems, 1993
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Gupta, K. C., Sarma, B. K.
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Gupta, K. C., Sarma, B. K.
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Fuzzy Sets and Systems, 1984
Analogues in the context of fuzzy topologies are obtained for a number of standard elementary results on topological groups, including preservation of openness under translation, an axiom system for a system of unit neighbourhoods, quotient and subgroup topologies, and the first isomorphism theorem.
Yu, Chunhai, Ma, Jiliang
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Analogues in the context of fuzzy topologies are obtained for a number of standard elementary results on topological groups, including preservation of openness under translation, an axiom system for a system of unit neighbourhoods, quotient and subgroup topologies, and the first isomorphism theorem.
Yu, Chunhai, Ma, Jiliang
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