FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS

نویسندگان
JAIN, APARNA ID 1

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

doi
10.22111/ijfs.2006.469
چکیده

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.

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