Convergent results about the use of fuzzy simulation in fuzzy optimization problems

We discuss the convergence of fuzzy simulation as it is employed in fuzzy optimization problems. Several convergence concepts for sequences of fuzzy variables are defined such as convergence in optimistic value. A new approach to approximating essentially bounded fuzzy variables with continuous possibility distributions is introduced. Applying the proposed approximation method to our previous work, we prove three convergence theorems about the use of fuzzy simulation in computing the credibility of a fuzzy event, finding the optimistic value of a return function, and calculating the expected value of a fuzzy variable.