Information Fusion And Numerical Characterization Of A Multi-source Information System

The complex data comes from different sources is often represented by a multi-source information system.With the coming of the Big data,in a multi-source information system,how to integrate complex data,measure its uncertainty and search for a compact subset of condition attributes have become one of the most important tasks.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.Rough set theory,originally proposed by Pawlak in 1982,is a powerful mathematical tool for addressing uncertain knowledge in a wide variety of applications machine learning,artificial intelligence,pattern recognition,and decision making.Similar to rough set theory,evidence theory and information theory are treated as important methods to deal with information fusion,uncertainty measurement and attribute reduction in intelligent systems.Pessimistic and optimistic multi-granulation fusion functions,provided by multigranulation rough set(MGRS)theory,which applied disjunctive and conjunctive operators to aggregate multiple granular structures induced by different binary relations,are too relax or too restrictive to solve the practical problems.Two-grade fusion algorithm used the well-defined granulation distance to divide the different granular structures into some groups.The division does not fully take each granular structure in multi-source information system into account.Whereas both of them seem not comprehensive enough to measure the uncertainty in multi-source environment.In this paper,innovative research and novel results are as follows:(1)By introducing the relationship between the MGRS theory and evidence theory,this paper discusses the essence and deficiency of MGRS.(2)In a multi-source information system,we propose the novel definitions of multisource rough approximation operators and corresponding multi-granulation rough approximation operators,probability distribution and basic probability assignment,then construct the connection between rough approximations and evidence theory.(3)Based on belief and plausibility functions,attribute reduction and corresponding numerical algorithm are developed.Finally,the above conclusions are extended to multisource coverings information system.(4)We propose a significance degree of condition attributes set with respect to sample,based on the probability distribution defined in Chapter 3,construct a novel definition of conditional probability,therefore design a probabilistic rough set,and consider the relationship with MGRS.Then,Shannon's fusion algorithm based on equivalence relations or coverings,involved in conditional probability and information entropy,is presented to calculate the uncertainty degree of a decision partition,respectively.And,a practical example is given to illustrate the advantages of this fusion approach.(5)By combing the discernibility matrix and distribution discernibility functions,we investigate the attribute reduction with variable precision rough set.The result of this study will be helpful for integrating the uncertain information come from multiple sources and eventful for creating a route of granular computing.