Belief Inaccuracy Information Measures and Their Extensions

This work introduces belief inaccuracy information (BII) and Jensen-belief inaccuracy information (JBII), grounded in the foundational concept of basic probability assignment. The significance of these novel methodologies lies in their potential to advance the field by providing valuable insights into belief accuracy assessment. The research not only establishes these measures but also highlights their relevance in addressing critical challenges within the realm of probability assignment. Further, some results associated with these proposed information measures were established. In addition, the BII and JBII measures were examined for escort and generalized escort of basic probability assignment functions, where an escort basic probability assignment with order α is constructed based on the power α of a baseline basic probability assignment with a normalizing constant. Finally, this paper presents compelling results derived from the application of BII and JBII measures. A detailed simulation of Conway's game of life cellular automaton is described, showcasing the utility of these measures in analyzing belief inaccuracies within complex dynamic systems. Furthermore, an application to ozone time series is explored, employing belief Kullback-Leibler and belief chi-square divergences. This application specifically focuses on the study of station discrepancies, revealing the versatility of the proposed measures in addressing diverse scenarios.