Independence and possibilistic conditioning. (English) Zbl 1004.60001

A probability theory with the conditional probability as basic concept has been developed by A. Rényi [“Foundations of probability” (1970; Zbl 0203.49801)] based on his paper [Acta Math. Acad. Sci. Hungar. 6, 285-333 (1955; Zbl 0067.10401)]; see also his [“Probability theory” (Elsevier, New York, 1970); translated from “Wahrscheinlichkeitsrechnung” (1962; Zbl 0102.34403), Ch. II, Sec. 11] among others. In the present paper and in three meeting contributions by the same authors [in: Proc. IPMU’2000 Conference, Madrid, 1561-1566 (2000), in: Workshop on Partial Knowledge and Uncertainty: Independence, Conditioning, Inference (Rome, 2000) and in: Technologies for constructing intelligent systems. 2. Stud. Fuzziness Soft Comput. 90, 59-71 (2002)] as well as in a paper by S. Coletti and R. Scozzafava [Soft Comput. 3, No. 3, 118-130 (1999)] a similar theory is offered with conditional possibility as basic concept. A substantial difference is that, while in the former the conditional probability \(P(A|B)\) is a function of two variables, the events \(A\) and \(B,\) here the “conditional event” \(A|B\) is defined, and the conditional possibility \(\Pi(A|B)\) is a function of this one variable. In addition, two possibility independence definitions and characterization theorems for conditional possibilities are offered, followed by particular cases.


60A05 Axioms; other general questions in probability
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.
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