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Constrained intervals and interval spaces

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Abstract

Constrained intervals, intervals as a mapping from [0, 1] to polynomials of degree one (linear functions) with non-negative slopes, and arithmetic on constrained intervals generate a space that turns out to be a cancellative abelian monoid albeit with a richer set of properties than the usual (standard) space of interval arithmetic. This means that not only do we have the classical embedding as developed by H. Radström, S. Markov, and the extension of E. Kaucher but the properties of these polynomials. We study the geometry of the embedding of intervals into a quasilinear space and some of the properties of the mapping of constrained intervals into a space of polynomials. It is assumed that the reader is familiar with the basic notions of interval arithmetic and interval analysis.

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Acknowledgments

This research has been sponsored, in part, by a grant from FAPESP 11/13985-0.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado Denver, Denver, USA

    Weldon A. Lodwick & Oscar A. Jenkins

  2. Departamento de Matemática Aplicada, UNESP, São José do Rio Preto, Brazil

    Weldon A. Lodwick

Authors
  1. Weldon A. Lodwick
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  2. Oscar A. Jenkins
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Corresponding author

Correspondence to Weldon A. Lodwick.

Additional information

Communicated by V. Kreinovich.

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Lodwick, W.A., Jenkins, O.A. Constrained intervals and interval spaces. Soft Comput 17, 1393–1402 (2013). https://doi.org/10.1007/s00500-013-1006-x

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  • DOI: https://doi.org/10.1007/s00500-013-1006-x

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