On The Correlations Between Fuzzy Variable And Its Application In Portfolio Selection

By employing the expected value operator of fuzzy variable,this thesis firstly defines two new correlation indices between two fuzzy variables, which are refered to as optimistic correlation and pessimistic correlation; Furthermore the optimistic covariance matrix and pessimistic covariance matrix of fuzzy vector are introduced, and the optimistic covariance matrix is proved to be positive semidefinite. Under the condition that the joint possibility distribution is the minimum of the marginal possibility distributions, the analytical expressions of optimistic covariance and pes-simistic covariance of the triangular, trapezoidal fuzzy variables are deduced. This thesis also applies the optimistic covariance matrix to portfolio problem with its convexity property, and the corresponding mean-optimistic covariance models are established. According to the property of optimistic covariance matrix, we can turn the proposed portfolio models into the quadratic convex programming. Finally, we provide numerical examples to illustrate optimistic covariance modeling ideas and effciency.The main contribution of this thesis contains the following four aspects:(ⅰ) the correlation of the fuzzy variables is defined, and some properties about corre-lations are discussed; (ⅱ) the analytical expressions of the triangular, trapezoidal fuzzy variable optimistic covariance and pessimistic covariance are given; (ⅲ) the mean-optimistic covariance models are established; (ⅳ) the cutting plane method is designed to solve the proposed models, and some numerical examples are provided to illustrate the new modeling ideas and the effectiveness of the proposed optimistic covariance method.