Information fusion and numerical characterization of a multi-source information system

The existing research of multi-source information system, pessimistic or optimistic multi-granulation fusion functions, provided by multi-granulation rough set (MGRS) theory, which apply disjunctive and conjunctive operators of multiple binary relations to aggregate multiple granular structures induced by different binary relations, are too relax or too restrictive to solve the practical problems. In this paper, we employ evidence theory, probability theory and information entropy to address the information fusion and numerical characterization of uncertain data in a multi-source information system (MSIS). First, we propose novel definitions of multi-source rough approximations and corresponding multi-granulation rough approximations, probability distribution and basic probability assignment, which can be used to construct the connection between rough approximations and evidence theory. Second, the above ideas are extended to multi-source covering information system (MCIS). Finally, Shannon's fusion algorithm based on equivalence relations or coverings, involved in the significance degree of condition attributes set with respect to a sample, conditional probability and information entropy, is presented to calculate the uncertainty degree of a decision, respectively. Then, based on the defined conditional probability in this paper, we design a multi-granulation variable precision rough set and consider the relationship with MGRS. And, the illustrative examples are given to elaborate the operation mechanism of the above conclusions. This study will be helpful for integrating the uncertain information come from multiple sources and eventful for creating a route of granular computing.