Fuzzy Probability Spaces and Their Applications in Decision Making 1 ...
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Fuzzy Probability Spaces and Their Applications in Decision Making Jana Talaˇsov´a and Ondˇrej Pavlaˇcka Palack´y University Olomouc, Czech Republic 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 ( 0} is called a support of A. Sets Aα = {x ∈ X|A(x) ≥ α}, α ∈ (0, 1], are called α-cuts of A. A set KerA = {x ∈ X|A(x) = 1} is a kernel of A. A fuzzy set A is called normal if KerA 6= ∅. The family of all fuzzy sets on X is denoted by F(X). A normal fuzzy set A on the set of all real numbers
