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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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Fuzzy groups, fuzzy functions and fuzzy equivalence relations
Fuzzy Sets and Systems, 2004To each fuzzy subgroup a fuzzy equivalence relation is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation. In the definition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp.
Demirci, M, Recasens Ferrés, Jorge
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Information Sciences, 1993
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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, 1999
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Frattini fuzzy subgroups of fuzzy groups
2019Este artículo continúa el estudio de la teoría de grupos difusos que se ha explorado a lo largo del tiempo. Proponemos subgrupos difusos máximos y subgrupos difusos de Frattini de grupos difusos como extensiones de subgrupos máximos y subgrupos de Frattini de grupos clásicos.
Paul Augustine Ejegwa, J. A. Otuwe
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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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