Conditional measures based on Archimedean semigroups
The starting point of our measure theory are \(\perp\)-decomposable measures m for crisp events, i.e. those characterized by the property \(m(A\dot\cup B)= m(A)\perp m(B)\) with respect to an Archimedean t-conorm \(\perp\). In the present paper we pay attention to the (NSA) case, i.e. where the measures can be transformed into probabilities. A generalized Bayesian model is presented based on inconditional and conditional decomposable measures (Section 1). Conditional measures as functions of the condition can be interpreted as fuzzy sets. Crisp and fuzzy valued measures for such fuzzy sets are discussed (Section 2). The model and the measures are applied to Sugeno's problem of buying residences (Section 3). The model is generalized (Section 4).
inconditional and conditional decomposable measures
scientific article; zbMATH DE number 4057863