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

Speaker: Vladik Kreinovich

Abstract

Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds on the measurement errors. In this case, based on the measurement result x^~, we can only conclude that the actual (unknown) value x of the desired quantity is in the interval [x^~ - delta; x^~ + delta]. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. To remedy this problem, in our previous papers, we proposed an extension of interval 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 talk, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary diff erential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time.