Approximating credibilistic constraints by robust counterparts of uncertain linear inequality

This paper studies a class of credibilistic optimization (CO) problems, in which a convex objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to discuss the robust counterpart approximations of ambiguous credibilistic constraints. Under mild assumptions, the closed property about the feasible region of credibilistic constraint is discussed. Using the obtained results, this paper deals with the robust counterpart approximations of credibilistic constraints under two types of ambiguity sets of possibility distributions. The first type is exponential function-based ambiguity set of possibility distribution, while the second type of ambiguity set is a particular case of the first one, and it is based on range and expectation information of fuzzy variables. The developed approximation techniques are capable to utilize the knowledge of ambiguity sets of possibility distributions when building distribution uncertainty-immunized solutions. As a result, the obtained safe approximations of ambiguous credibilistic constraints are computationally tractable convex/linear constraints. To apply the proposed approximation approach, a portfolio optimization problem is addressed, in which the investor is to find a portfolio to maximize the value-at-risk of his total return under the support and expectation information of uncertain returns. We use two types of robust counterpart approximations to credibilistic constraints. The computational results support our arguments.