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RESEARCH PRODUCT

Conditional measures and their applications to fuzzy sets

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Abstract Given a ⊥-decomposable measure with respect to a continuous t-conorm, as introduced by the author in an earlier paper (see Section 1), we can construct ⊥-conditional measures as implications. These fulfil a ‘generalized product law’ replacing the product in the classical law by any other strict t-norm ⊥ and turn out to be decomposable with respect to an operation ⊥ V depending on ⊥, ⊥ and the condition set V (Section 2). More general, conditional measures are introduced axiomatically and are shown to be ⊥-conditional measures with respect to some ⊥-decomposable measure (Section 3). ‘Bayesian-like’ models are given which are alternatives to that presented by the author in a recent paper (Section 4). Finally, some applications to fuzzy sets are sketched (Section 5).