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Differentiations in Hierarchical Fuzzy Systems

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Recent Developments and the New Direction in Soft-Computing Foundations and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 361))

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Abstract

Hierarchical fuzzy systems are one of the most popular solutions for the curse of dimensionality problem occurred in complex fuzzy rule based systems with a large number of input parameters. Nevertheless these systems have a hidden inaccuracy and instability problem. In detail, the outputs of hierarchical systems, based on Mamdani style inference, differ from the outputs of equivalent single system. Moreover they are not stable in any variation of system modeling even if the rules and membership functions do not expose any differentiation. This paper revisits inaccuracy and instability problems of hierarchical fuzzy inference systems. It investigates the differentiation in systems’ behaviors against the variations in system modeling, and provides a pattern to identify the magnitude of this differentiation.

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Gazi University, Ankara, Turkey

    Begum Mutlu

  2. Department of Computer Engineering, Hacettepe University, Ankara, Turkey

    Ebru A. Sezer

Authors
  1. Begum Mutlu
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  2. Ebru A. Sezer
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Corresponding author

Correspondence to Begum Mutlu .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  2. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

  3. Department of Information Technology and Programming, Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

  4. Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Z. Reformat

  5. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

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Mutlu, B., Sezer, E.A. (2018). Differentiations in Hierarchical Fuzzy Systems. In: Zadeh, L., Yager, R., Shahbazova, S., Reformat, M., Kreinovich, V. (eds) Recent Developments and the New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-319-75408-6_28

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  • DOI: https://doi.org/10.1007/978-3-319-75408-6_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75407-9

  • Online ISBN: 978-3-319-75408-6

  • eBook Packages: EngineeringEngineering (R0)

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