An approach to ordinal decision making

Abstract

We describe the problem of decision making under ignorance and discuss the need of introducing a decision attitude or disposition in solving this problem. We show the OWA operators provide a general framework for evaluating the alternatives when the payoffs are numeric values. We then turn to the problem of decision making when the payoffs are linguistic values drawn from an ordinal scale. A solution to this problem is then suggested using an ordinal version of the OWA aggregation method. We emphasize the role of the OWA weighting vector as a means for introducing the decision maker's attitude and investigate the representation of various prototypical decision attitudes. Two measures are provided for classifying the OWA weighting vectors used in the aggregations. The first of these measures is the degree of optimism implied by the vector. The second measures the degree of dispersion associated with the vector. In this work the interpretation of the decision making attitude, via the OWA weighting vector, as a kind of probability distribution is highlighted. In particular the ith component in the vector is interpreted as the probability that the ith best outcome will occur. This view helps unify the problems of decision making under ignorance and decision making under uncertainty and allows us to see the evaluation of an alternative, in both cases, as the formulation of an expected value. Furthermore this interpretation leads to a viewing of the measure of dispersion as a kind of entropy. In the ordinal environment this leads to the development of a new measure of entropy for ordinal probabilities.