A belief Hellinger distance for D–S evidence theory and its application in pattern recognition

Abstract

Dempster–Shafer (D–S) evidence theory has been studied and applied broadly, owing to its advantage of effectively handling uncertainty problems in multisource information fusion. But under the circumstance of the body of evidences are highly conflicting, the result of evidence fusion is not so satisfactory even counter-intuitive. In order to conquer the flaw, a newly defined belief Hellinger distance is presented to quantify the discrepancy between evidences in D–S evidence theory. The belief Hellinger distance takes the number of the possible hypotheses into account, thus allowing it to provide a more rational and telling approach for dissimilarity measure between evidences. In addition, through strictly proven, the belief Hellinger distance meets the properties of boundedness, nondegeneracy, symmetry and satisfaction of triangle inequality, which is to say it is a true metric. On the basis of newly defined belief Hellinger distance, a new multisource information fusion method is well-designed. What is more, an iris dataset-based and a motor rotor fault diagnosis application are implemented to verify the new proposed distance measurement and the multisource information fusion method has an extensive practicality, effectiveness and applicability.