A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems

Abstract

This paper presents a new parametrized family of joint possibility distributions that can be used to control the Pompeiu–Hausdorff norm of the sum resulting from the extension principle. We are able to generate sums with norms covering the entire interval ranging from the smallest possible value to the largest one. Finally, we apply our approach to numerical methods for solving first-order fuzzy initial value problems.