This paper investigates some fundamental questions involving additions of interactive fuzzy numbers. The notion of interactivity between two fuzzy numbers, say A and B, is described by a joint possibility distribution J. One can define a fuzzy number A+j B (or A - jB), called J-interactive sum (or difference) of A and B, in terms of the sup-J extension principle of the addition (or difference) operator of the real numbers. In this article we address the following three questions: (1) Given fuzzy numbers B and C, is there a fuzzy number X and a joint possibility distribution J of X and B such that X +j B = C? (2) Given fuzzy numbers A, B, and C, is there a joint possibility distribution J of A and B such that A+jB = C? (3) Given a joint possibility distribution J of fuzzy numbers A and B, is there a joint possibility distribution N of (A +j B) and B such that (A +j B) -_N B = A? It is worth noting that these questions are trivially answered in the case where the fuzzy numbers A, B and C are real numbers, since the fuzzy arithmetic +j and - n are extension of the classical arithmetic for real numbers.
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