How Much For a Set: General Case of Decision Making Under Set-Valued Uncertainty

Authors

Laxman Bokati, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-1-2021

Comments

Technical Report: UTEP-CS-21-05b

Published in Julia Rayz, Victor Raskin, Scott Dick, and Vladik Kreinovich (eds.), Explainable AI and Other Applications of Fuzzy Techniques, Proceedings of the Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2021, West Lafayette, Indiana, June 7-9, 2021, Springer, Cham, Switzerland, 2022, pp. 52-61.

Abstract

In real life, we often need to make a decision, i.e., we need to select one of the possible alternatives. In many practical situations, our objective is financial: we need to select an alternative that will bring us the largest financial gain. The problem is that usually, we only know the gain corresponding to each alternative with some uncertainty: instead of the exact numerical value of this gain, there is a whole set of possible values of this gain. How can we make decisions under such interval-valued uncertainty? An answer to this question is known for the case when these sets are closed. In this paper, we extend this result of the general case, when sets are not necessarily closed.