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On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations

Author

Listed:
  • Luciano Stefanini

    () (Department of Economics, Università di Urbino "Carlo Bo")

  • Maria Letizia Guerra

    () (Department of Mathematics for Social and Economic Sciences, University of Bologna and Department of Economics, Università di Urbino "Carlo Bo")

Abstract

We analyze a decomposition of the fuzzy numbers (or intervals) which seems to be of interest in the study of some properties of fuzzy arithmetic operations and, in particular, in the analysis of fuzziness, of shape-preservation (symmetry) and distributivity of multiplication and division. By the use of the same decomposition, we suggest an approximation of multiplication and division to reduce the overestimation e?ect and/or to obtain total-distributivity of multiplication and left-distributivity of division. Finally, we compare the proposed approximation with the results of standard (a-cuts based) fuzzy mathematics and with other new definitions of fuzzy arithmetic operations that recently appeared in the literature.

Suggested Citation

  • Luciano Stefanini & Maria Letizia Guerra, 2007. "On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations," Working Papers 0703, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
  • Handle: RePEc:urb:wpaper:07_03
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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_07_03.pdf
    File Function: First version, 2007
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    Citations

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    Cited by:

    1. Luciano Stefanini & Barnabás Bede, 2012. "Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations," Working Papers 1208, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    2. Barnabás Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.

    More about this item

    Keywords

    Fuzzy Sets; Fuzzy Calculus; fuzzy arithmetic operations;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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