Measure, Integrals and Fuzzy Events

This chapter reviews classical measure theory including probability and Lebesgue measures. This discussion is followed by fuzzy measures, Sugeno measures, and possibilistic measures in order to understand the integration of Lebesgue, Choquet and Sugeno. These concepts are used in the development of fuzzy expected value. Lastly, the chapter closes with a discussion of the concepts of fuzzy event, the probability of a fuzzy event, dependence of fuzzy events, independence of fuzzy events, together with the concepts of random linguistic variables and random fuzzy variables.