Abstract
In evidence theory, Dempster’s rule of combination is the most commonly applied method to aggregate bodies of evidence obtained from different sources to make a decision. However, when multiple independent bodies of evidence with conflict are aggregated by Dempster’s rule of combination, the counterintuitive results can be generated. Evidence discounting is proved to be an efficient way to eliminate the counterintuitive combination results. Following the discounting ideas, a new combination approach based on fuzzy discounting is put forward. Both the conflict between bodies of evidence and the uncertainty of a body of evidence itself are taken into account to determine the discounting factors. Jousselme’s evidence distance is used to represent conflict between bodies of evidence, and discriminability measure is defined to represent uncertainty of a body of evidence itself. Consider that both the evidence distance and the discriminability measure are semantically fuzzy. Thus, fuzzy membership functions are defined to describe both of them, and a fuzzy reasoning rule base is constructed to derive the discounting factors. Numerical examples indicate that this new combination approach proposed can achieve fast convergence speed and is robust to disturbing evidences, i.e., it is an effective method to process conflicting evidences combination.
Highlights
Multisource information fusion is being more and more applied in many areas
A new combination approach based on fuzzy discounting is put forward
According to the above analysis, the procedure to aggregate evidences by combination approach based on fuzzy discounting can be concluded as follows: (1) Calculate evidence distance dJ between each body of evidence and others and discriminability measure (DM) of each body of evidence itself; (2) Calculate membership of dJ and DM; (3) Carry out fuzzy reasoning according to fuzzy rule base to derive discounting factors; (4) Discount bodies of evidence by discounting factors; (5) Aggregate discounted evidences by Dempster’s rule of combination to obtain the final result
Summary
Multisource information fusion is being more and more applied in many areas. Usually, the data acquired from various sources are uncertain or imprecise to some extent. Undesirable results may be generated when aggregating conflicting bodies of evidence by Dempster’s rule of combination. To address this problem when applying Dempster’s rule, there are two views. The other view holds that the problem can be caused by evidence model rather than the combination rule, and a series of combination approaches based on revising evidence (Li et al 2016a; Zhang and Mu 2016; Xue et al 2018; Zhang and Deng 2019) are put forward. A combination approach based on fuzzy discounting is put forward Both the conflict between a body of evidence and others and the uncertainty of a body of evidence itself are taken into account in this method. Definition 3 Suppose that m is a BPA defined on H and a is a discounting factor, m is discounted by a which can be depicted as follows: maðXÞ 1⁄4
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