The schnittaxiom and unions of fuzzy subgroups

doi:10.1016/0020-0255(93)90078-Z

Information Sciences

Volume 70, Issue 3, 1 June 1993, Pages 213-220

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Abstract

A necessary and sufficient condition for the union of an arbitrary family of fuzzy subgroups of a group to be a fuzzy group has been proposed. The criterion which gives a cut of the unit interval is called the Schnittaxiom. It has been applied successfully to investigate fuzzy subgroupness of arbitrary unions of homomorphic images and preimages.

References (4)

P.S. Das
Fuzzy groups and level subgroups
J. Math. Anal. Appl.
(1981)
N.P. Mukherjee et al.
Fuzzy normal subgroups and fuzzy cosets
J. Inform. Sci.
(1984)

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Cited by (1)

Union of fuzzy subgroups
1996, Fuzzy Sets and Systems
In this paper, we completely answer the question raised by Dixit et al. (1990) regarding union of fuzzy subgroups. Moreover, we provide a simple necessary and sufficient condition for the union of an arbitrary family of fuzzy subgroups to be a fuzzy subgroup. Without using Schnitt axiom, we provide straightforward proofs of fuzzy subgroupness of arbitrary union of homomorphic images and preimages.

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Information Sciences

The schnittaxiom and unions of fuzzy subgroups

Abstract

Fuzzy groups and level subgroups

J. Math. Anal. Appl.

Fuzzy normal subgroups and fuzzy cosets

J. Inform. Sci.

Union of fuzzy subgroups