Fuzzy Powergroups,

With developing fuzzy mathematics, the importance of set value mapping has been highlighted, so that the upgrade of all kinds of the structures, such as or- dered, topological measurable structure, etc, have been considered. The concept of HX group was raised firstly in the [23 studied normal FIX group and uniform I-{X group. The properties, structures, classifications, homomorphism and isomorphism of all kinds of FIX group have been considered in the pa t6J12J th per . With e development of fuzzy set theory, all kinds of the structure ar upgraded not only from their universes to their power sets but aTho from their universes to their fuzzy power sets. In the paperJ, the concept of fuzzy power group has been raised firstly and the structure and homomorphisms of fuzzy pow- er group has been considered. On the basis of paper], this paper gives some further description for fuzzy power group. First, the properties of the fuzzy power group wiil be considered. second, the structures of each fuzzy power group will be described systematically, and attempts will be made to classify the fuzzy power groups and the chains of subgroup and the chains of normal subgroup of each class will be constructed. Fi- nally it homorphism, isomorphism and direct product will be considered.