CONDITIONAL MEASURES AND THEIR APPLICATIONS TO FUZZY-SETS

Given a perpendicular-to-decomposable measure with respect to a continuous t-conorm, as introduced by the author in an earlier paper (see Section 1), we can construct inverted-perpendicular-conditional measures as implications. These fulfil a 'generalized product law' replacing the product in the classical law by any other strict t-norm inverted-perpendicular and turn out to be decomposable with respect to an operation inverted-perpendicular(v) depending on perpendicular-to, inverted-perpendicular and the condition set V (Section 2). More general, conditional measures are introduced axiomatically and are shown to be inverted-conditional measures with respect to some perpendicular-to-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).