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Using Special Structured Fuzzy Measure to Represent Interaction Among IF-THEN Rules

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Advances in Machine Learning and Cybernetics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3930))

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Abstract

When fuzzy IF-THEN rules are used to approximate reasoning, interaction exists among rules. Handling the interaction based on a non-integral can lead to an improvement of reasoning accuracy but the determination of non-linear integral usually needs to solve a linear programming problem with too many parameters when the rules are a little many. That is, the number of parameters increases exponentially with the number of rules. This paper proposes a new approach to denoting the interaction by a 2-additive fuzzy measure which replaces the general set function of the old non-linear integral approach. The number of parameters determined in the new approach is greatly less than the number of parameters in the old approach. Compared with the old approach, the new one has a little loss of accuracy but the new approach reduces the number of parameters from an exponential to polynomial quantity.

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Authors and Affiliations

  1. Machine Learning Center, Faculty of Mathematics and Computer Science, Hebei University, Baoding, 071002, China

    Xi-Zhao Wang & Jun Shen

Authors
  1. Xi-Zhao Wang
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  2. Jun Shen
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Editor information

Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, P.O. Box, Hong Kong, China

    Daniel S. Yeung

  2. School of Creative Media, City University of Hong Kong,, China

    Zhi-Qiang Liu

  3. Department of Mathematics and Computer Science, Hebei University, 071002, Baoding, Hebei, P.R. China

    Xi-Zhao Wang

  4. School of Electrical and Information Engineering, University of Sydney, 2006, NSW, Australia

    Hong Yan

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© 2006 Springer-Verlag Berlin Heidelberg

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Wang, XZ., Shen, J. (2006). Using Special Structured Fuzzy Measure to Represent Interaction Among IF-THEN Rules. In: Yeung, D.S., Liu, ZQ., Wang, XZ., Yan, H. (eds) Advances in Machine Learning and Cybernetics. Lecture Notes in Computer Science(), vol 3930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11739685_48

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  • DOI: https://doi.org/10.1007/11739685_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33584-9

  • Online ISBN: 978-3-540-33585-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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