APARNA JAIN - DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE, UNIVERSITY OF DELHI, NEW DELHI, INDIA

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

Fuzzy subgroup, Equivalence relation, Lattice, alpha– cut, Strong alpha– cut, homomorphism