Controlling the width of the sum of interactive fuzzy numbers with applications to fuzzy initial value problems

Abstract

Arithmetic operations on fuzzy numbers are usually performed using Zadeh's extension principle. The amount of uncertainty expressed in the resulting fuzzy number tends to be much higher than the amounts of uncertainty in the operands. This effect is often undesired and does not reflect reality if there is interactivity between the operands. We recently presented an approach for adding fuzzy numbers using an extension principle based on a parametrized family of joint possibility distributions. In this paper, we employ this approach in order to derive a method for controlling the uncertainty given by the width, i.e., the length of the support, of the resulting sum of fuzzy numbers.