From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs Under Interval, P-Box, and Fuzzy Uncertainty

Authors

Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Andrzej Pownuk, The University of Texas at El PasoFollow
Barnabas Bede

Publication Date

5-2009

Comments

UTEP-CS-06-50d.

Short version published in: Patricia Melin, Oscar Castillo, Luis T. Aguilar, Janusz Kacprzyk, and Witold Pedrycz (eds.), Foundations of Fuzzy Logic and Soft Computing, Proceedings of the World Congress of the International Fuzzy Systems Association IFSA'2007, Cancun, Mexico, June 18-21, 2007, Springer Lecture Notes on Artificial Intelligence, 2007, Vol. 4529, pp. 33-42; full version published in in JinTao Yao (ed.), Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation, IGI Global Publisher, 2010, pp. 131-147.

Abstract

In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. In our previous papers, we proposed an extension of this technique to set computations, where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time.