Some Analytical Properties of Expected Values of Fuzzy Variables with Parameters

In many fuzzy programming problems, the objectives and constraints may consist of some expected values of prescribed fuzzy variables. Therefore, analyzing the properties of those expected values is helpful to solving the problems. The objective of this paper is to deal with some analytical properties of expected values of fuzzy variables with parameters. First, some continuity theorems are derived for the properties of continuity and semicontinuity of the expected values. Then, a differentiation formula of the expected value with respect to the parameter is established. The results obtained in this paper are useful in fuzzy programming models.