Probability of a fuzzy event: An axiomatic approach
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TL;DR
Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh based on the postulate that the sum of the conditional probability and its complement given any fuzzy event adds to one or on soft independence for orthogonal sets with independent constitutive elements.
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.