POSSIBILITY THEORY I: THE MEASURE- AND INTEGRAL-THEORETIC GROUNDWORK

Possibility Theory I the Measure- and Integral-theoretic Groundwork

In this paper, I provide the basis for a measureand integral-theoretic formulation of possibility theory. It is shown that, using a general definition of possibility measures, and a generalization of Sugeno’s fuzzy integral – the seminormed fuzzy integral, or possibility integral –, a unified and consistent account can be given of many of the possibilistic results extant in the literature. The ...

Measure-Theoretic Probability I

Decision-theoretic foundations of qualitative possibility theory

This paper presents a justiication of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with a set of acts equipped with a complete preordering relation. Conditions on acts are given that imply ...

Integral geometry – measure theoretic approach and stochastic applications

Integral geometry, as it is understood here, deals with the computation and application of geometric mean values with respect to invariant measures. In the following, I want to give an introduction to the integral geometry of polyconvex sets (i.e., finite unions of compact convex sets) in Euclidean spaces. The invariant or Haar measures that occur will therefore be those on the groups of transl...

The distributional Henstock-Kurzweil integral and measure differential equations

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...