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;Vladik Kreinovich;Andrzej Pownuk;Barnabás Bede

  • Affiliations:

  • Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA;Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA;Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA;Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA

  • Venue:
  • IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
  • Year:
  • 2007

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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.