Abstarct: Aabstract In this thesis, fuzzy entropy in fuzzy spaces and its applications in financial mathematics are investigated. This review deals with the mean-variance and skewness multi-objective model with Borg entropy and fuzzy efficiency for portfolio optimization, portfolio selection baxsed on fuzzy cross entropy and portfolio optimization. We interpret fuzzy concepts, validity theory, Shannon entropy, fuzzy simulation, hybrid intelligent algorithm and genetic algorithm GA and some other cases.