A Family of Joint Possibility Distributions for Adding Interactive Fuzzy Numbers Inspired by Biomathematical Models

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 γ for a given pair of fuzzy numbers, say A1 and A2, such that the norm of the corresponding sums of A1 and A2 form a increasing mapping with respect to γ.