# FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS

Document Type : Research Paper

Author

DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE, UNIVERSITY OF DELHI, NEW DELHI, INDIA

Abstract

In this paper, we study an equivalence relation on the set of fuzzy
subgroups of an arbitrary group G and give four equivalent conditions each of
which characterizes this relation. We demonstrate that with this equivalence
relation each equivalence class constitutes a lattice under the ordering of fuzzy set
inclusion. Moreover, we study the behavior of these equivalence classes under the
action of a group homomorphism.

Keywords

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