Abstract

Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribu-tion ( J). An approach based on the sup -J extension principle, which is a generalization of Zadeh's extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup -J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh's extension.