Elsevier

Fuzzy Sets and Systems

Volume 149, Issue 2, 16 January 2005, Pages 369-381
Fuzzy Sets and Systems

Conditional probability on MV-algebras

https://doi.org/10.1016/j.fss.2004.04.010Get rights and content

Abstract

An appropriate definition of a conditional probability on an MV-algebra was an open problem mentioned in Riečan and Mundici (Handbook of Measure Theory, North-Holland, Amsterdam, 2002). We propose some concept of conditional probability (state) on a σ-complete MV-algebra with product. Its basic properties will be proven and it will also be demonstrated that the conditional probability in classical probability theory is a special case of this definition. Moreover, the paper contains also a discussion of the interpretation of fuzzy sets and conditioning in fuzzy probability theory.

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