Fuzzy Equivalence Relation Of Fuzzy Rough Group

Connected Rough structure with Algebra structure, Topology structure and order structure, many new prosperous mathematics branches will appear currently, there have been some articles on connecting Rough structure with Algebra structure. Rough ideals in a semigroups, Rough ideals been first introduced by KuroKi N. Under the condition of the congruence relation, Rough sets of a subsemigroup was proved to be its subsemigroup , while that of a left (right, besides ) ideals was also proved to be its a left (right, besides ) ideals, next, Rough sets in a group first introduced. Under the condition of the congruence relation determined by a given normal subgroup in a group, Rough sets of a subgroup was proved to be its subgroup, while that of a normal one was also proved to be its normal subgroup. Connected Rough structure with Fuzzy Algebra structure, there also have been some articles on connecting Rough structure with Fuzzy Algebra structure by zhang Jinglin. Under the condition of the congruence relation determined by a given Fuzzy normal group in a group, Rough sets of a Fuzzy subgroup was proved to be its Fuzzy subgroup, while that of a Fuzzy normal group was also proved to be its a Fuzzy normal group.In this paper, under the condition of the Fuzzy congruence relation determined by a given Fuzzy normal subgroup in a group, Connecting Rough structure with Algebra structure was discussed. It is proved that Under the condition of the fuzzy congruence relation determined by a given Fuzzy normal subgroup in a group, Rough sets of a Fuzzy subgroup was a Fuzzy subgroup, while that of a Fuzzy normal group was also proved to be its a Fuzzy normal group. Next T fuzzy congruence relation, T fuzzy Rough sets properties been first introduced in this paper and get some similar results.