Uncertain measure of permutable uncertain event

Abstract

Probability theory and uncertainty theory are two different types of mathematical systems to describe indeterminacy containing randomness and uncertainty, respectively. To be precise, the former is used to model randomness associated with frequency via probability measure, while the latter is used to model human uncertainty associated with belief degree by means of uncertain measure. This paper aims at investigating the uncertain measure of permutable uncertain event which is an uncertain zero-one law as the counterpart of Hewitt and Savage zero-one law in probability theory.