Decision making with imprecise probabilities and its application

Experimental evidence has repeatedly shown that the widely used principle of maximization of expected utility has serious shortcomings. Non-expected utility theory suggests more adequate models. However, in these models utility functions and probabilities are mainly considered as real-valued functions whereas in reality human preferences are imprecise being described in natural language (NL). Nowadays a methodology for dealing with second-order uncertainty, or uncertainty² is not available, whereas, real-world uncertainties mainly fall into this category. In this paper we present an effective decision theory under uncertainty² when the environment of fuzzy events and fuzzy states are characterized by imprecise probabilities. The proposed theory includes a non-expected fuzzy utility function represented by a fuzzy integral with fuzzy-number-valued fuzzy measure generated by imprecise probabilities. The suggested theory encompasses the classical utility based decision analysis, cumulative Prospect theory and Choquet expected utility on bipolar scales. We apply this methodology for solving a real-life business problem.