Uncertain systems are universal approximators

Abstract

Uncertain inference is a process of deriving consequences from uncertain knowledge or ev-idences via the tool of conditional uncertain set. Based on uncertain inference, uncertain system is a function from its inputs to outputs. This paper proves that uncertain systems are universal approxi-mators, which means that uncertain systems are capable of approximating any continuous function on a compact set to arbitrary accuracy. This result can be viewed as an existence theorem of an optimal uncertain system for a wide variety of problems.