Interval Order Relations Research Articles

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 α-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.

Ranking fuzzy interval numbers in the setting of random sets

A new approach to the problem of extending interval order relations to the case of fuzzy interval numbers is presented. In the approach, the connectedness between fuzzy sets and random sets is used. Finally, eight different fuzzy order relations are given. Some formal properties of these relations are investigated, and the problem of computing the values of their membership functions discussed. For trapezoidal fuzzy interval numbers, the formulae depend on the parameters from which these numbers are derived.