| MV-algebra is a kind of logic algebra, which has been introduced by the international famous model expert C. C. Chang. It was introduced to solve testify of the infinite value Lucasiewicz logical completeness theory, and this completeness can be reduced as the completeness about the MV algebras. MV-algebra has attracted quite a few scholars' interest since the last 50s'. There are many important relations between MV-algebra and fuzzy implication algebra introduced by Wu Wangming, lattice implication algebra introduced by Xu Yang, the BCK algebra introduced by Japanese scholar, BL-algebra and R0 algebra. And more and more scholars are interested in MV-algebra. Some scholar began to propose the probability measure in MV-algebra in the last 90s', as well as they began to study the content related with the probability measure. But it is still not systemic for many questions. We still need to improve it. There are few papers that comprehensively involve the conditional probably and conditional expectation in China. And it is still blank for the research of the probability in MV-algebra. It has an important theoretic meaning to study the above-mentioned problem. This paper tries to discuss the probability, conditional probability and conditional expectation on MV-algebra of fuzzy sets.Based on the above-mentioned study background and compared with the Kolmogorov model used the theory of modern analysis, analytical probability and martingale convergence theory, this paper does the works as following:1. Perfect the properties of the probability on MV-algebra.2. Discuss two kind of independence of observables on MV-algebra and introduce the sufficient and necessary condition for one of the two independences.3. Discuss the properties about the conditional probability and the conditional independence.4. Discuss the properties about the conditional expectation.For convenience , all properties are discussed in a prototype of MV-algebra—the family of all fuzzy events.
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