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Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with 13 some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and more general semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such… (More)

In this article we provide a detailed study of basic properties of the smallest universal integral IS with S being the underlying semicopula and review some of the recent developments in this direction. The class of in-tegrals under study is also known under the name seminormed integrals and includes the well-known Sugeno as well as Shilkret integral as… (More)

In this paper we continue studying the smallest universal integral IS having S as the underlying semicopula. We present convergence theorems for IS-integral sequences including monotone, almost everywhere, almost uniform, in measure and in mean converging sequences of measurable functions, respectively. It emerges that these convergences characterize the… (More)

Real world applications often require dealing with the situations in which the exact numerical values of the (sub)measure of a set may not be provided, but at least some probabilistic assignment still could be done. Also, several concepts in uncertainty processing are linked to the processing of distribution functions. In the framework of generalized… (More)

Several concepts of approximate reasoning in uncertainty processing are linked to the processing of distribution functions. In this paper we make use of prob-abilistic framework of approximate reasoning by proposing a Lebesgue-type approach to integration of non-negative real-valued functions with respect to probabilistic-valued decomposable (sub)measures.… (More)

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