How to Make Decision Under Interval Uncertainty: Description of All Reasonable Partial Orders on the Set of All Intervals

Authors

Tiago M. Costa, Universidad de TarapacáFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-1-2023

Comments

Technical Report: UTEP-CS-23-29a

To appear in Proceedings of the 20th World Congress of the International Fuzzy Systems Association IFSA'2023, Daegu, South Korea, August 20-24, 2023.

Abstract

In many practical situations, we need to make a decision while for each alternative, we only know the corresponding value of the objective function with interval uncertainty. To help a decision maker in this situation, we need to know the (in general, partial) order on the set of all intervals that corresponds to the preferences of the decision maker. For this purpose, in this paper, we provide a description of all such partial orders -- under some reasonable conditions. It turns out that each such order is characterized by two linear inequalities relating the endpoints of the corresponding intervals, and that all such orders form a 2-parametric family.