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A survey of credibility theory

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Abstract

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.

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  1. Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Baoding Liu

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Liu, B. A survey of credibility theory. Fuzzy Optim Decis Making 5, 387–408 (2006). https://doi.org/10.1007/s10700-006-0016-x

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