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On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations

Listed author(s):
  • 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")

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.

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File Function: First version, 2007
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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 0703.

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Length: 19 pages
Date of creation: 2007
Date of revision: 2007
Handle: RePEc:urb:wpaper:07_03
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