fuzzy projective modules and tensor products in fuzzy module categories

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mod}$ and get some unexpected results. in addition, we prove that$mbox{hom}(xi_p,-)$ is exact if and only if $xi_p$ is a fuzzy projective $r$-module, when $r$ is a commutative semiperfect ring.finally, we investigate tensor product of two fuzzy $r$-modules and get some related properties. also, we study the relationships between hom functor and tensor functor.