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Fuzzy Sets and Systems, 1996
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A. M. Abd-Allah, R. A. K. Omar
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A. M. Abd-Allah, R. A. K. Omar
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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 Sets and Systems, 2001
Based on a modification of the concept of metric fuzziness given by \textit{I. Kramosil} and \textit{J. Michálek} [Kybernetica, Praha 11, 336-344 (1975; Zbl 0319.54002)], \textit{A. George} and \textit{P. Veeramani} [Fuzzy Sets Syst. 64, No. 3, 395-399 (1994; Zbl 0843.54014)] introduced and studied a notion of fuzzy metric space which permits to extend
Salvador Romaguera, Manuel Sanchis
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Based on a modification of the concept of metric fuzziness given by \textit{I. Kramosil} and \textit{J. Michálek} [Kybernetica, Praha 11, 336-344 (1975; Zbl 0319.54002)], \textit{A. George} and \textit{P. Veeramani} [Fuzzy Sets Syst. 64, No. 3, 395-399 (1994; Zbl 0843.54014)] introduced and studied a notion of fuzzy metric space which permits to extend
Salvador Romaguera, Manuel Sanchis
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A note on fuzzy relations and fuzzy groups
Information Sciences, 1991The paper characterizes groups G such that for any fuzzy subgroup R of \(G\times G\) the formula \(A_ R(x)=\sup_{y\in G}\min (R(x,y),R(y,x))\) gives a fuzzy subgroup of G. This corrects a result of \textit{P. Bhattacharya} and \textit{N. P. Mukherjee} [Inf. Sci. 36, 267-282 (1985; Zbl 0599.20003), Theorem 4.7].
D. S. Malik, John N. Mordeson
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Information Sciences, 1993
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Fuzzy Sets and Systems, 1999
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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.
Cong-Hua Yan, Sheng-zhang Guo
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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.
Cong-Hua Yan, Sheng-zhang Guo
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Fuzzy Sets and Systems, 1995
A fuzzy group \((G,\mu)\) is said to be continuous if \(G\) is a topological group and \(\mu: G\to [0,1]\) is continuous. The author defines a topological group \(G\) to be fuzzy trivial if all continuous functions \(\mu\) from \(G\) to \([0,1]\) such that \(\mu\) is a fuzzy subgroup of \(G\) are constants.
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A fuzzy group \((G,\mu)\) is said to be continuous if \(G\) is a topological group and \(\mu: G\to [0,1]\) is continuous. The author defines a topological group \(G\) to be fuzzy trivial if all continuous functions \(\mu\) from \(G\) to \([0,1]\) such that \(\mu\) is a fuzzy subgroup of \(G\) are constants.
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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)].
N. P. Mukherjee, Prabir Bhattacharya
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On fuzzy spaces and fuzzy group theory
Information Sciences, 1994The notion of fuzzy set was generalized in many directions, e.g.: \(L\)-fuzzy sets [\textit{J. A. Goguen}, J. Math. Anal. Appl. 18, 145--174 (1967; Zbl 0145.24404)], probabilistic sets [\textit{K. Hirota}, Fuzzy Sets Syst. 5, 31--36 (1981; Zbl 0442.60008)], intuitionistic fuzzy sets [\textit{K. Atanassov}, Fuzzy Sets Syst.
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