A Characterization of fuzzy product and coproduct modules

A Characterization of Fuzzy Product and Coproduct Modules In this study, fuzzy module homomorphisms on the completely distributed complete lattices and the relation between fuzzy module homomorphisms and fuzzy submodules have been established. It has been shown that, the fuzzy product and coproduct have the universal property by characterizing the fuzzy product and coproduct of t - level in the category of modules. After the introduction to the fuzzy logic, some relations between sets and fuzzy sets has been investigated. The first section of chapter 3 is in a preliminary form to the next chapter. Here, the structure of fuzzy subgroups, fuzzy subrings and fuzzy ideals have been considered. In section 3.2., the fuzzy module homomorphisms have been discussed and the theorems in classical homomorphisms have been carried to the fuzzy module homomorphism. In addition definition of kernel and image of a fuzzy module homomorphism have been given and it has been observed that these are submodules. In addion, the relation between fuzzy module homomorphism and fuzzy submodules has been characterized by a theorem. Finally, after the definitions of fuzzy product and coproduct oft-level in the category of modules, some theorems concerning these concepts have been proved. Key Words: Fuzzy function, fuzzy logic, fuzzy homomorphism, fuzzy product and coproduct. HI