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A unified algebraic structure for uncertain reasonings

  • Xudong Luo
  • Chengqi Zhang
Neural Nets and Uncertainity II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1114)

Abstract

This paper identifies an axiom foundation for uncertain reasonings in rule-based expert systems: a near topological algebra (NT-algebra for short), which holds some basic notions hidden behind the uncertain reasoning models in rule-based expert systems. In according with basic ways of topological connection in an inference network, an NT-algebraic structure has five basic operators, i.e. AND, OR, NOT, Sequential combination and Parallel combination, which obey some axioms. An NT-algebraic structure is defined on a near-degree space introduced by the authors, which is a special topological space. The continuities of real functions, of fuzzy functions and the functions in other sense can be uniformly considered in the framework of a near-degree space. This paper also proves that the EMYCIN's and PROSPECTOR'S uncertain reasoning models correspond to good NT-algebras, respectively. Compared to other related works, the NT-algebra as an axiom foundation has the following characteristics: (1) various cases of assessments for uncertainties of both evidence and rules are put into a unified algebraic structure; and (2) major emphasis has been placed on the basic laws of the propagation for them in an inference network.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Xudong Luo
    • 1
  • Chengqi Zhang
    • 1
  1. 1.Department of Mathematics, Statistics and Computing ScienceThe University of New EnglandArmidaleAustralia

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