The concept of conditional fuzzy measure

In this article a concept of conditional fuzzy measure is presented, which is a generalization of conditional probability measure. Its properties are studied in the general case and in some particular types of fuzzy measures as representable measures, capacities of order two, and belief-plausibility measures. In the case of capacities of order two it coincides with the concept given by Dempster for representable measures. However, it differs from the Dempster's rule for conditioning belief-plausibility measures. As it is shown, Dempster's rule of conditioning is based on the idea of combining information and our definition is based on a restriction in the set of possible worlds.