On a Descriptive Model of a Measurable Value Function under Uncertainty for Complex Decision Analysis

In this paper a descriptive extension of the expected utility model to account for various paradoxes is proposed using the concept of strength of preference. We deal with the case where probability of occurrence for each event is unknown. When we describe the degree of ignorance and uncertainty by the basic probability of Dempster-Shafer theory, the problem is how to represent the value of a set element to construct a measurable value function under uncertainty based on this concept. For identifying a value function under uncertainty, we need to find the preference relations among set elements, which is not an easy task. If the number of elements contained in the set element contains considerbale number of elements, it is not practical to find the value function as a function of the set elements. To cope with this difficulty we use some appropriate axiom of dominance.