In many models for real-world problems such as the law of conservation of energy, the sum of parameters must be zero. In this paper, we investigate the problem of adding fuzzy numbers using the extension principle based on the concept of the joint possibility distribution. In particular, we present a formula to produce a family of joint possibility distribution indexed by a parameter gamma for a given pair of fuzzy numbers, say A(1) and A(2), such that the norm of the corresponding sums of A(1) and A(2) form a increasing mapping with respect to gamma.89 13181323