What Is Fuzzy Probability Theory?

Abstrac t . A basic theory of fuzzy probability is presented. It is shown that many of the concepts of standard (crisp) probability theory carry over to the fuzzy context. Borrowing some terminology from quantum mechanics, we call a fuzzy event an effect and a fuzzy random variable an observable. Pattern recognition instruments are discussed and are used to motivate the theory. The probability that an effect occurs and the distribution of an observable are defined. The basic connectives for effects are presented and their elementary properties are given. Joint observables are studied. Conditional probabilities, conditional expectations and independence of effects and observables are discussed. The Borel-Cantelli lemma and laws of large numbers are proved and it is noted that the central limit theorem holds in thiá context.