A general measure of uncertainty-based information.

摘要

This document describes the measure of uncertainty of a fuzzy body of evidence in a data fusion system. Mathematical theories of uncertainty are now well established. Among them, evidence theory can address discord and nonspecificity, called ambiguity; and fuzzy set theory can address fuzziness and nonspecificity, called imprecision. A theory that combines evidence theory and fuzzy set theory can address all kinds of uncertainty. Our objective is to find a measure in fuzzy evidence theory, which includes all kinds of uncertainty.; The innovations presented in this work are as follows: (1) We give some justifications for reducing the computation of Aggregate Uncertainty measure (AU) to the core of the corresponding belief function, and propose an algorithm to calculate AU(Bel) which reduces the computing complexity of the MRW algorithm as proposed by A. Meyerowitz et al. We prove that this algorithm leads to the same results as Meyerowitz's, and give conditions under which it significantly reduces the computing complexity. (2) In order to overcome the shortcomings (complicated, insensitive, difficult to distinguish two kinds of uncertainty) an alternative measure to AU for quantifying ambiguity of belief functions is proposed. This measure, called Ambiguity Measure (AM), besides satisfying all the requirements for general measures, also overcomes some of the shortcomings of AU. (3) A new measure, called General Measure (GM) is proposed, and it includes all kinds of uncertainty. We give the definition of GM, and we show that GM defined on fuzzy evidence theory, will be AM in evidence theory and imprecision measure (including fuzziness and nonspecificity) in fuzzy set theory under some conditions. A simulation method is also proposed.