An approximation to the extension principle using decomposition of fuzzy intervals

This article presents a proposal for the decomposition of large ranges of uncertainty associated with the Cartesian product of two fuzzy intervals. We compute an approximation of the fuzzy set obtained by applying extension principle to a real function by means of this decomposition and piecewise linearization of the function. It is proved the efficiency of the method via convergence in D-metric. We also extend the method to the case when the function has more than two arguments. Some examples are included to illustrate the proposed method and to compare it with others.