Using Fuzzy Probability Weights in Cumulative Prospect Theory

During the past years, a rapid growth has been seen in the descriptive approaches to decision choice. As opposed to normative expected utility theory, these approaches are based on the subjective perception of probabilities by the individuals, which takes place in real situations of risky choice. The modelling of this kind of perceptions is made on the basis of probability weighting functions. In cumulative prospect theory, which is the focus of this paper, decision prospect outcome weights are calculated using the obtained probability weights. If the value functions are constructed in the sets of positive and negative outcomes, then, based on the outcome value evaluations and outcome decision weights, generalised evaluations of prospect value are calculated, which are the basis for choosing an optimal prospect. In cumulative prospect theory, all relevant evaluations are represented in deterministic form. The present research is an attempt to extend classical prospect theory to the cases when the weights of probabilities are given in a fuzzy form.