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RESEARCH PRODUCT

Conditioning for Boolean Subsets, Indicator Functions and Fuzzy Subsets

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This chapter deals with measure-free conditioning. It starts with the mean value based definition of conditional fuzzy subsets which again gives a fuzzy subset. Applying this general construction to indicator functions, it is proved that these conditionals form an MV-algebra and that this is isomorphic to the already known MV-algebra of the interval based conditional Boolean subsets. In the following, the problem of iteration is completely solved with the result that there are exactly two types of iteration, called the blurred resp. the sharper one, which remain in the corresponding MV-algebras. Moreover, the general concept of conditional operators plays a significant role. Finally, the problem of extending an uncertainty measure is discussed.