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Generation and Reduction of Fuzzy Sets with PG-Means and Fuzzy Similarity Measures

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Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 749))

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Abstract

The probabilistic clustering techniques can be applied to generate fuzzy sets in situations where there is little or no information about data. Quite often, they generate a huge number of clusters. These clusters can be interpreted as fuzzy sets in a process of building a fuzzy system. A large number of fuzzy sets introduce noise to the fuzzy system, hence the need to reduce their number. Fuzzy Similarity Measures (FSMs) are widely used for comparison of fuzzy sets. Multiple FSMs have been proposed so far, but identifying a single FSM that is the most suitable for a given task is not always a straightforward process. On many occasions, FSMs are used to reduce a number of fuzzy sets. In this paper, we present the results of analyzing suitability of FSMs to reduce number of fuzzy sets and fuzzy if-then rules for an image segmentation problem. We use a PG-Means algorithm to generate fuzzy sets on both input and output variables. We propose and apply algorithms utilizing FSMs to reduce the number of fuzzy sets and rules. The paper includes a case study investigating the application of the proposed method on two images.

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Notes

  1. 1.

    A comprehensive analysis of FSM is presented in the paper ‘Experimental Evaluation and Comparison of Fuzzy Similarity Measures’ to be submitted to IEEE Transactions of Fuzzy Systems.

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Acknowledgements

The authors would like to thank prof. Greg Hamerly, from the Baylor University, for letting them use the PG-Means program he developed with Yu Feng [38].

Author information

Authors and Affiliations

  1. CINVESTAV, Computer Science, Zapopan, Jalisco, Mexico

    Arturo Garcia-Garcia & Andres Mendez-Vazquez

  2. University of Alberta, Edmonton, Canada

    Marek Z. Reformat

Authors
  1. Arturo Garcia-Garcia
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  2. Andres Mendez-Vazquez
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  3. Marek Z. Reformat
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Corresponding author

Correspondence to Arturo Garcia-Garcia .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  2. Division of Graduate Studies and Research , Tijuana Institute of Technology , Tijuana, Baja California, Mexico

    Patricia Melin

  3. Systems Research Institute, Polish Academy of Sciences , Warszawa, Poland

    Janusz Kacprzyk

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Garcia-Garcia, A., Mendez-Vazquez, A., Reformat, M.Z. (2018). Generation and Reduction of Fuzzy Sets with PG-Means and Fuzzy Similarity Measures. In: Castillo, O., Melin, P., Kacprzyk, J. (eds) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications. Studies in Computational Intelligence, vol 749. Springer, Cham. https://doi.org/10.1007/978-3-319-71008-2_22

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  • DOI: https://doi.org/10.1007/978-3-319-71008-2_22

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-71008-2

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