FUZZY-QUOTIENT GROUPS

The operation of a group G induces, through Zadeh's extension principl e, a semigroup operation on I(G). We define a fuzzy-quotient group of G to be a fuzzy partition of G that is a subsemigroup of I(G) having a group structure. We show that fuzzy-quotient groups of G are in one-t o-one correspondence with normal fuzzy subgroups of G, and that their associated fuzzy similarity relations are all two-sided-in-variant. We study relationships between the level structures of these structures. We also give a necessary and sufficient condition for a group homomor phism to factor through fuzzy quotients.