Abstract

The article begins with a discussion of sets and fuzzy sets. It is observed that identifying a set with its indicator function makes it clear that a fuzzy set is a direct and natural generalization of a set. Making this identification also provides simplified proofs of various relationships between sets. Connectives for fuzzy sets that generalize those for sets are defined. The fundamentals of ordinary probability theory are reviewed and these ideas are used to motivate fuzzy probability theory. Observables (fuzzy random variables) and their distributions are defined. Some applications of fuzzy probability theory to quantum mechanics and computer science are briefly considered