Probability of a fuzzy event: An axiomatic approach |
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Authors: | Philippe Smets |
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Institution: | Laboratory of Medical Statistics, School of Public Health, Brussels Free University (U.L.B.), 1070 Brussels, Belgium |
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Abstract: | Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh. They are based (1) on the postulate that the sum of the conditional probability of a fuzzy event and of its complement given any fuzzy event adds to one or (2) on soft independence for orthogonal sets with independent constitutive elements. A general postulate is also required concerning the complement of a fuzzy set. The classical definition of the operator representing the complement can also be deduced. |
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Keywords: | Probability Fuzzy event Complement |
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