On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations

Luciano Stefanini () and Maria Letizia Guerra ()

No 703, Working Papers from University of Urbino Carlo Bo, Department of Economics

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.

Keywords: Fuzzy Sets; Fuzzy Calculus; fuzzy arithmetic operations (search for similar items in EconPapers)
JEL-codes: C00 C60 C63 D80 (search for similar items in EconPapers)
Date: 2007, Revised 2007
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