Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions

Abstract

In this article we propose a method to calculate the sum and difference of two interactive fuzzy numbers. These arithmetic operations are obtained by the sup-J extension principle, which is a generalization of the Zadeh's extension principle. We show that the proposed addition and subtraction produce fuzzy numbers with smaller width and norm than any other addition and subtraction for fuzzy numbers, obtained by joint possibility distributions. Moreover, we provide a characterization of these operations by means of α-cuts. We compare the proposed interactive addition with the standard one. We also establish connections among the proposed subtraction and the Hukuhara, generalized Hukuhara and generalize differences. Finally, we provide an application in the Malthusian Model in order to illustrate the results.