Towards faster estimation of statistics and ODEs under interval, P-Box, and fuzzy uncertainty: From interval computations to rough set-related computations

Abstract

Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds Δ on the measurement errors. 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. In this paper, we show that one way to remedy this problem is to extend interval technique to rough-set computations, where at each stage, in addition to intervals of possible values of the quantities, we also keep rough sets representing possible values of pairs (triples, etc.). The paper's outline is as follows: we formulate the main problem (Section 1), briefly overview interval computations techniques solve this problem (Section 2), and then explain how the main ideas behind interval computation techniques can be extended to computations with rough sets (Section 3). © 2011 Springer-Verlag.