How Probabilistic Methods for Data Fitting Deal with Interval Uncertainty: A More Realistic Analysis

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Sergey P. Shary, Novosibirsk UniversityFollow

Publication Date

11-1-2021

Comments

Technical Report: UTEP-CS-21-102

Abstract

In our previous paper, we showed that a simplified probabilistic approach to interval uncertainty leads to the known notion of a united solution set. In this paper, we show that a more realistic probabilistic analysis of data fitting under interval uncertainty leads to another known notion -- the notion of a tolerable solution set. Thus, the notion of a tolerance solution set also has a clear probabilistic interpretation. Good news is that, in contrast to the united solution set whose computation is, in general, NP-hard, the tolerable solution set can be computed by a feasible algorithm.