Logic Value Fuzzy Subgroup Of a Group

The aims of this article are to establish the relationship between the fuzzy algebra and the classical logic and to study fuzzy algebra by the use of classical logic methods. We firstly introduces the concept of the logic value fuzzy subgroup, and studies the relationship between the fuzzy subgroup and its dual. It is pointed out that H is a logic value(normal) fuzzy subgroup of a group G if and only if for all value assignment v, the core and the v- dual of H is the (normal) subgroup of G. Secondly, we study the properties of the logical value fuzzy subgroup, the logical value normal fuzzy subgroup and its quotient groups. Finally, We study the properties of homomorphic image of the logic value fuzzy subgroup. The research of this paper can help to establish the relationship between the fuzzy algebra and the classical logic.