Fuzzy Power Group On Hypergroup

With the development of fuzzy set theory, all kinds of the structure are upgraded not only from their universes to their power sets but also from their universes to their fuzzy power sets. In the paper [8] , the concept of fuzzy power group has been raised firstly and the structure and homomor-phism of fuzzy power group has been considered.In this paper, hypergroups are upgraded to their fuzzy power sets, the concept of fuzzy power group on hypergroup is introduced.In the firstly part, the background and development of fuzzy power group is summarized and the concepts, properties and part of conclusions of fuzzy power group and hypergroup are introduced; in the secondly part , the concept of fuzzy power group on hypergroup is presented, and the characters and structure of fuzzy power group on hypergroup are discussed, especially the structures of fuzzy power group on quasicanonical hypergroup; finally, the problem of homomorphism of fuzzy power group on hypergroup is presented, and some related theorems results are derived.