Negation of Basic Probability Assignment: Trends of Dissimilarity and Dispersion

In the field of knowledge representation, negation has been introduced so that practical issues can be modelled more effectively. The negation of probability was first formally determined by Zadeh, with its basic properties proposed by Yager. Recent studies have extended the negation of probability to that of basic probability assignment (BPA) by introducing Dempster-Shafer theory which is believed to perform well in dealing with uncertainty problems. Besides, the negation model has been proved to have the maximum entropy allocation, which attracts studies on uncertainty measures that can be applied in the negation process. In this paper, we have mainly investigated the trend of dissimilarity between two BPAs in the negation process. In particular, an evidence distance proposed by Jousselme et al. is used to serve as a dissimilarity measure to help quantify the variation trends. Moreover, standard deviation is used in this study to represent the dispersion in a BPA. Through our analysis, we obtained some interesting properties finally with their generalizations discussed in a proposed framework of negation methods.