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Fuzzy normal subgroups and fuzzy cosets. (English) Zbl 0568.20002

The concept of fuzzy subgroup [cf. A. Rosenfeld, J. Math. Anal. Appl. 35, 512-517 (1971; Zbl 0194.055); P. S. Das, J. Math. Anal. Appl. 84, 264-269 (1981; Zbl 0476.20002)] is investigated. Several (fuzzy type) extensions of known results for normal subgroups, quotient groups and finite groups are obtained.
Reviewer: J.Drewniak

MSC:

20A05 Axiomatics and elementary properties of groups
20E07 Subgroup theorems; subgroup growth
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References:

[1] P. Bhattacharya, Fuzzy subgroups: Some characterisations, J. Math. Anal. Appl.; P. Bhattacharya, Fuzzy subgroups: Some characterisations, J. Math. Anal. Appl. · Zbl 0631.20002
[2] P. Bhattacharya, Fuzzy subgroups: Some characterisations II, submitted for publication.; P. Bhattacharya, Fuzzy subgroups: Some characterisations II, submitted for publication.
[3] Das, P. S., Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84, 264-269 (1981) · Zbl 0476.20002
[4] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35, 512-517 (1971) · Zbl 0194.05501
[5] A. Rosenfeld, Fuzzy graphs, in Fuzzy Sets and Their Applications; A. Rosenfeld, Fuzzy graphs, in Fuzzy Sets and Their Applications
[6] (Yager, R. R., Fuzzy Sets and Possibility Theory (1982), Pergamon: Pergamon New York)
[7] Zadeh, L. A., Fuzzy sets, Inform and Control, 8, 338-353 (1965) · Zbl 0139.24606
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