Fuzzy Optimization and Decision Making

, Volume 5, Issue 4, pp 387–408 | Cite as

A survey of credibility theory

  • Baoding LiuEmail author


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.


Fuzzy variable Credibility measure Credibility theory Fuzzy random variable Random fuzzy variable Conditional credibility 


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© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Uncertainty Theory Laboratory, Department of Mathematical SciencesTsinghua UniversityBeijingChina

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