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Article information
2026 , Volume 31, ¹ 3, p.86-95
Kreinovich V., Shary S.P.
Probabilistic analysis of interval data fitting: justification of the tolerable solution set
In our previous article, it was shown that a simplified probabilistic approach to describing interval uncertainty in the data fitting problem leads to the concept of the united solution set. In this paper, we show that a more realistic probabilistic analysis of the problem under interval uncertainty makes it necessary to use another well-known concept — the tolerable solution set. Thus, the tolerable solution set obtains a clear probabilistic interpretation. Unlike the united solution set, whose recognition and estimation are generally NP-hard problems, the tolerable solution set for the linear case is recognized and estimated by feasible algorithms with polynomial complexity.
Keywords: interval, interval uncertainty, interval equations system, united solution set, tolerable solution set, probabilistic uncertainty
Author(s):
Kreinovich Vladik
Professor
Position: Professor
Office: University of Texas of El Paso
Address: 79968, USA, El Paso, 500, W. University
Phone Office: (915) 747-6951
E-mail: vladik@utep.edu
Shary Sergey Petrovich
Dr.
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
Phone Office: (383) 330 86 56
E-mail: shary@ict.nsc.ru
SPIN-code: 9938-9344
Bibliography link:
Kreinovich V., Shary S.P. Probabilistic analysis of interval data fitting: justification of the tolerable solution set // Computational technologies. 2026. V. 31. ¹ 3. P. 86-95
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