On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations

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