Utility maximization problem using curve trapezoidal fuzzy number

The fuzzy set theory has been widely used to solve many practical problems. By using fuzzy approaches, quantitative analysis, qualitative analysis, subjective opinions can better integrated into model based uncertainty. In this paper we have considered a technique for solving an optimal control problem with fuzzy constraints. The possibility distribution function of a fuzzy variable is usually defined by the membership function of the corresponding fuzzy set. We used a curve-type trapezoidal fuzzy number and membership function. Then we propose constrained fuzzy optimization problem by maximizing portfolio utility. Finally, we illustrate this approach with numerical example.