Fuzzy sets and probability: misunderstandings, bridges and gaps
- 30 December 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 5, 1059-1068
- https://doi.org/10.1109/fuzzy.1993.327367
Abstract
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.Keywords
This publication has 46 references indexed in Scilit:
- Naturalized logic and chain setsInformation Sciences, 1991
- Approximate reasoning: Past, present, futureInformation Sciences, 1991
- Epistemic entrenchment and possibilistic logicArtificial Intelligence, 1991
- The concept of conditional fuzzy measureInternational Journal of Intelligent Systems, 1990
- On fuzzy syllogismsComputational Intelligence, 1988
- Bayesian and non-bayesian evidential updatingArtificial Intelligence, 1987
- The Axioms of Subjective ProbabilityStatistical Science, 1986
- Ma\e auf unscharfen MengenProbability Theory and Related Fields, 1976
- On the analytic formalism of the theory of fuzzy setsInformation Sciences, 1973
- Theory of capacitiesAnnales de l'institut Fourier, 1954