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A survey of credibility theory. (English) Zbl 1133.90426
Summary: This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.
MSC:
90C70Fuzzy programming
03E72Fuzzy set theory
60A05Axioms of probability theory
62A01Foundations and philosophical topics in statistics
68T37Reasoning under uncertainty
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