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Combining Linear Equation Models via Dempster’s Rule

  • Liping Liu
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)

Abstract

This paper proposes a concept of imaginary extreme numbers, which are like traditional complex number a + bi but with i = \(\sqrt{-1}\) being replaced by e = 1/0, and defines usual operations such as addition, subtraction, and division on the numbers. It applies the concept to representing linear equations in knowledge-based systems. It proves that the combination of linear equations via Dempster’s rule is equivalent to solving a system of simultaneous equations or finding a least-square estimate when they are overdetermined.

Keywords

Linear Equation Belief Function Moment Matrix Usual Operation Nonzero Real Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Dempster, 2001]
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    Liu, L.: Dempster’s rule for combining linear models. Technical report, Department of Management, The University of Akron, Akron, Ohio (2011a)Google Scholar
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    Liu, L.: A new rule for combining linear belief functions. Technical report, Department of Management, The University of Akron, Akron, Ohio (2011b)Google Scholar
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    Liu, L., Shenoy, C., Shenoy, P.P.: Knowledge representation and integration for portfolio evaluation using linear belief functions. IEEE Transactions on Systems, Man, and Cybernetics, Series A 36(4), 774–785 (2006)CrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Liping Liu
    • 1
  1. 1.The University of AkronAkronUSA

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