Fuzzy sets and probability: misunderstandings, bridges and gaps

One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets. The literature pertaining to this debate is surveyed. The authors address some classical misunderstandings between fuzzy sets and probabilities. They consider probabilistic interpretations of membership functions that may help in membership function assessment. Nonprobabilistic interpretations of fuzzy sets are identified. The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified. Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed