Decision making theory with imprecise probabilities

Summary form only given. There is an extensive literature on decision-making under uncertainty. Unfortunately, up to day there are no valid decision principles. The widely used principle of maximization of expected utility has serious shortcomings. The first approach in classical theory of choice was formulated axiomatically in the expected utility theory of von Neumann and Morgenstern and is the predominant economic theory for decision making under uncertainty. In another, more advanced approach of Savage subjective expected utility it is assumed that peoples assess the state of the economy and the effects of their behavior in a forward-looking way by processing available information according to standard statistical principles. We present a characterization theorem on existence of a fuzzy utility function representing weak order relation defined over the set of fuzzy alternatives. We also develop an effective decision theory with imprecise probabilities when the environment of fuzzy events, fuzzy states, fuzzy relations, and fuzzy constraints are characterized by imprecise probabilities.