DECISION THEORY WITH IMPRECISE PROBABILITIES

Abstract

There is an extensive literature on decision making under uncertainty. Unfortunately, up to date there are no valid decision principles. Experimental evidence has repeatedly shown that widely used principle of maximization of expected utility has serious shortcomings. Utility function and nonadditive measures used in nonexpected utility models are mainly considered as real-valued functions whereas in reality decision-relevant information is imprecise and therefore is described in natural language. This applies, in particular, to imprecise probabilities expressed by terms such as likely, unlikely, probable, etc. The principal objective of the paper is the development of computationally effective methods of decision making with imprecise probabilities. We present representation theorems for a nonexpected fuzzy utility function under imprecise probabilities. We develop an effective decision theory when the environment of fuzzy events, fuzzy states, fuzzy relations and fuzzy constraints are characterized by imprecise probabilities. The suggested methodology is applied for a real-life decision-making problem.