Evidence Theory and Its Applications

Jiwen Guan · D. A. Bell

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Multi-Criteria Decision Making Logic, Reasoning, and Knowledge Bayesian Modeling and Causal Inference

Abstract

Refining frames of discernment. Partitioning a frame of discernment. The inner and outer coarsening mappings. Coarsening the composition of refinings. Mathematical summary. Support functions. Coarsening the evidential functions. Coarsening mappings and evidential functions. Support mass functions. Mathematical summary. Coarsening operations and mappings. Coarsening operations and orthogonal sum. Relevant interaction of the evidence. Compositions of coarsening operations. Mathematical summary. Refining evidential functions. Refining evidential functions. Coarsenings and evidential functions. Refining operation and the orthogonal sum. Mathematical summary. Refining and coarsening operations. Coarsening refined functions. Refining coarsened functions. Refining and coarsening operations. Mathematical summary. Time linearization for a tree. A review of Barnett's time linearization. Extending from singletons to subsets. The Gordon-Shortliffe tree hierarchy. The Shafer-Logan technique. Mathematical summary. Computations from the bottom up. The first reduction - subroutine 3. The first reduction - subroutine 2. Mathematical summary. Local computation for middle nodes. The second reduction - subroutine 1. The second reduction - subroutine 2. The third reduction - subroutines 1 and 2. The final reduction - subroutine 1. Mathematical summary. Local computations from the bottom. The computation from bottom to top. An example of computation from the bottom. Computations from the top down. Nodes outside the current sub-branch. An equation to solve local computations. Global computation of the orthogonal sum. Framework of the computation from root. Mathematical summary. Computing from the root. The first stage of a round - subroutine 4. The second stage of a round - subroutine 5. The third stage of a round - subroutine 6. Mathematical summary. Finishing the downward computation. The second round - subroutines 4,5 and 6. A summary and the complexity analysis. Completing our example of computation. Mathematical summary. Bibliography. Index.

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