Approximate fuzzy arithmetic operations using monotonic interpolations

We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+,−, ·, :) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic functions are then used to define a parametric representation of a large class of fuzzy numbers having general shapes of the membership function and a simple and accurate procedure is introduced for the fuzzy arithmetic. Several computational experiments are given to show the good performance of the proposed procedure.