Fuzzy Decision Matrices in Case of a Discrete Underlying Fuzzy Probability Measure
Decision matrices represent a common tool for solving decision-making problems under risk. Elements of the matrix express the outcomes if a decision-maker chooses the particular alternative and the particular state of the world occurs. We deal with the problem of extension of a decision matrix to the case of fuzzy states of the world and fuzzy outcomes of alternatives. We consider the approach based on the idea that a fuzzy decision matrix determines a collection of fuzzy rule-based systems. The aim of the paper is to study extension of this approach to the case where the states of the world are fuzzy sets on the finite universal set and the probabilities of elementary events are determined by a tuple of fuzzy probabilities. We derive the formulas for computations of the fuzzy expected values and fuzzy variances of the outcomes of alternatives, based on which the alternatives can be compared.
KeywordsDecision matrices Decision-making under risk Fuzzy probability measure Fuzzy states of the world Fuzzy rule-based systems
The paper is supported by the grant IGA_PrF_2017_019 Mathematical Models of the Internal Grant Agency of Palacký University Olomouc. The support is greatly acknowledged.
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