A dissimilarity measure based on singular value and its application in incremental discounting

A new dissimilarity measure between two basic probability assignments (BPA) is proposed. With this method, two BPA's are represented by a two-row matrix called BPA matrix. Along with a similarity matrix of focal elements to maintain the original relations between focal elements, the smallest singular value of the modified BPA matrix is taken as the dissimilarity measure between two BPA's. It satisfies several basic properties and has good behaviors in lots of situations. Therefore this new dissimilarity measure is used in place of the conflict coefficient in an incremental discounting method so as to improve its performance. The incremental discounting method allows us to discount sources to different levels according to predefined overall conflicts. And a direct discounting method can be seen as a special case of the incremental one. Numerical examples show effectiveness of this new proposed method.