Abstarct: Entropy is used as a measure to characterize the uncertainty. In this thesis, we review the uncertain space and state some of its properties. In the following, we introduce triangular entropy and cross entropy for uncertain variable and partial triangular entropy and elliptic entropy for uncertain random variable and give some mathematical properties for the entropies. As an application, we consider portfolio selection problem using entropy. Numerical results show that the portfolio weighted by the partial triangular mean-variance-entropy model has the best performance among the presented models.