The expected value of a function of a fuzzy variable with a continuous membership function

In this paper, a formula for the expected value of a function of a fuzzy variable is presented, with which the exact expected value of the function of the fuzzy variable can be obtained directly. The proposed formula holds provided that the function is monotonic, oil the assumption that the fuzzy Variable has a continuous membership function. Furthermore, some examples showing how to apply the formula are given. (C) 2007 Elsevier Ltd. All rights reserved.