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A generalization of Hukuhara difference for interval and fuzzy arithmetic

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Author Info

  • Luciano Stefanini

    ()
    (Department of Economics and Quantitative Methods, University of Urbino (Italy))

Abstract

We propose a generalization of the Hukuhara difference. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is seggested to attempt a generalization of division for real intervals and fuzzy numbers.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_01.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 0801.

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Length: 13 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:urb:wpaper:08_01

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Web page: http://www.econ.uniurb.it/
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Related research

Keywords: Fuzzy Arithmetic; Interval Arithmetic; Hukuhara difference; Fuzzy Numbers.;

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Cited by:
  1. Luciano Stefanini & Barnabas Bede, 2008. "Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations," Working Papers, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 0803, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  2. Luciano Stefanini & Barnabás Bede, 2012. "Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations," Working Papers, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 1208, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
  3. Luciano Stefanini & Barnabás Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
  4. Barnabás Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.

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