Ranking of admissible alternatives in interval decision making

In the framework of interval decision making, the available information is vague and numerically imprecise, and decision situations are modelled by imprecise probabilities and utilities that are simply represented by suitable intervals and comparisons. Alternatives are therefore evaluated in terms of interval expected utilities, which are then used for expressing crisp preferences among these alternatives. In this work, we construct a valued preference relation expressing the degree to which an alternative is considered as better than another alternative, based on the overlap between these interval expected utilities. In particular, we study a chain of interval order relations associated with the proposed valued preference relation and introduce the notion of a-admissibility in terms of non-dominated alternatives induced by such relations. Furthermore, we consider a possible ranking of the admissible alternatives w.r.t. the corresponding degrees of preference/dominance. In addition, the decision maker is provided with the possibility to state a threshold, expressing his/her own ideas, understanding, views, etc., based upon which an alternative can be regarded as better than another one. Thus the admissible alternatives can be defined as non-dominated alternatives w.r.t. the stated degree of preference.