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Possibility theory. II: Conditional possibility. (English) Zbl 0955.28013
Summary: In Part II it is shown that the notion of conditional possibility can be consistently introduced in possibility theory, in very much the same way as conditional expectations and probabilities are defined in the measure- and integral-theoretic treatment of probability theory. I write down possibilistic integral equations which are formal counterparts of the integral equations used to define conditional expectations and probabilities, and use their solutions to define conditional possibilities. In all, three types of conditional possibilities, with special cases, are introduced and studied. I explain why, like conditional expectations, conditional possibilities are not uniquely defined, but can only be determined up to almost everywhere equality, and I assess the consequences of this nondeterminacy. I also show that this approach solves a number of consistency problems, extant in the literature.
See also the preceding summary of Part I and the summary of Part II below.

28E10 Fuzzy measure theory
03B48 Probability and inductive logic
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
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