Fuzzy Probability Spaces and Their Applications in Decision Making

Abstract

In this paper, two types of fuzzy probability spaces will be introduced and their applications in methods of decision making under risk (especially in the Decision Matrix Method) will be described. First, a fuzzy probability space that generalizes the classical probability space (Rn; Bn; p) to the situation of fuzzy random events will be studied. It will be applied to perform fuzzy discretization of continuous risk factors. Second, a fuzzy probability space that enables an adequate mathematical modelling of expertly set uncertain probabilities of states of the world will be defined. The presented theoretical results will be illustrated with two examples comparing stock yields.