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On some relation between fuzzy probability measure and fuzzy P-measure. (English) Zbl 0588.60005
The definitions of fuzzy probability measure and fuzzy P-measure are given. The other definitions include the cumulative distribution function, fuzzy interval, and the fuzzy relation ”less or equal”.
The correspondence between the fuzzy P-measure and the fuzzy distribution function is established. It is demonstrated that for each fuzzy probability measure m there exists a unique fuzzy P-measure P such that \[ P(\phi [-\infty,x[)=m(\phi [-\infty,x[). \] Since the fuzzy P-measure is the unique fuzzy probability measure satisfying the Bayes formula, the connection between fuzzy probability measure and fuzzy P-measures makes the Bayes formula applicable for any fuzzy probability space defined by E. P. Klement, W. Schwyhla and R. Lowen [Fuzzy Sets Syst. 5, 21-30 (1981; Zbl 0447.28005)].
Reviewer: Y.Qu

60A99 Foundations of probability theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)