The modified Dempster-Shafer approach to classification

Dale J. Fixsen · Ronald Mahler

119 citations0/0 files storedIEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans

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Multi-Criteria Decision Making Bayesian Modeling and Causal Inference Rough Sets and Fuzzy Logic

Abstract

This paper describes "modified Dempster-Shafer" (MDS), an approach to object identification which incorporates Bayesian prior distributions into an altered Dempster-Shafer rule of combination. The MDS combination rule reduces, under strong independence assumptions, to a special case of Bayes' rule. We show that MDS has rigorous probabilistic foundations in the theory of random sets. We also demonstrate close relationships between MDS and Smets' "pignistic" probabilities (1990), which in the MDS framework become true posterior distributions. We describe the application of MDS to a practical classification algorithm which uses an information-theoretic technique to limit the combinatorial explosion of evidence. We also define a non-ad hoc, MDS-based classification "miss distance" metric used to measure the performance of this algorithm.

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References

1993Entropy optimization principles with applications 1990Constructing the Pignistic Probability Function in a Context of Uncertainty 1978On random sets and belief functions 1987Properties of measures of information in evidence and possibility theories 1990Consonant approximations of belief functions 1991On the justification of Dempster's rule of combination 1987Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?

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2013How to preserve the conflict as an alarm in the combination of belief functions?2005Shedding new light on Zadeh's criticism of Dempster's rule of combination 2013On the Validity of Dempster's Fusion Rule and its Interpretation as a Generalization of Bayesian Fusion Rule 1996Combining ambiguous evidence with respect to ambiguous a priori knowledge. I. Boolean logic 2007Information Affinity: A New Similarity Measure for Possibilistic Uncertain Information 2005The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making

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