UNCERTAINTY IN THE DEMPSTER-SHAFER THEORY: A CRITICAL RE-EXAMINATION

George J. Klir · Arthur Ramer

172 citations0/0 files storedInternational Journal of General Systems

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Multi-Criteria Decision Making Rough Sets and Fuzzy Logic Fuzzy and Soft Set Theory

Abstract

Measures of two types of uncertainty that coexist in the Dempster-Shafer theory are overviewed. A measure of one type of uncertainty, which expresses nonspecificity of evidential claims, is well justified on both intuitive and mathematical grounds. Proposed measures of the other types of uncertainty, which atlempt to capture conflicts among evidential claims, are shown to have some deficiencies. To alleviate these deficiencies, a new measure is proposed. This measure, which is called a measure of discord, is not only satisfactory on intuitive grounds, but has also desirable mathematical properties. A measure of total uncertainty, which is defined as the sum of nonspecificity and discord, is also discussed. The paper focuses on conceptual issues. Mathematical properties of the measure of discord are only slated; their proofs are given in a companion paper.15

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1965Fuzzy sets 1983ENTROPY AND SPECIFICITY IN A MATHEMATICAL THEORY OF EVIDENCE 1987Properties of measures of information in evidence and possibility theories

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2017Uncertainty measure in evidence theory with its applications 2017A new definition of entropy of belief functions in the Dempster–Shafer theory 2019An Improved Deng Entropy and Its Application in Pattern Recognition 2002Entropy of discrete Choquet capacities 1996QUANTIFICATION OF CONFLICT IN DEMPSTER-SHAFER FRAMEWORK: A NEW APPROACH 1993Uncertainty measures for evidential reasoning II: A new measure of total uncertainty 2016Analyzing properties of Deng entropy in the theory of evidence 2018An evidential Markov decision making model

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