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Sensitivity analysis of fuzzy rule-based classification systems by means of the Lipschitz condition

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Abstract

The fuzzy rule-based classifier can be taken as a function that assigns to a point from the feature space a class, or a class with an association degree. Under this assumption, the robustness of fuzzy rule-based classifiers is investigated by means of the Lipschitz condition. The Lipschitz continuity of fuzzy sets, fuzzy rules and whole fuzzy rule-based classifiers is examined for multi-polar outputs, extended multi-polar outputs and outputs in the form of a class. Related performance of a fuzzy rule-based classifier is also discussed. All studied concepts are shown on an exemplar fuzzy rule-based classifier.

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Acknowledgments

I would like to thank the editor and two anonymous reviewers for their valuable comments. This work was supported by grants VEGA 2/0049/14, APVV-0073-10 and Program Fellowship of SAS.

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Correspondence to Andrea Mesiarová-Zemánková.

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Communicated by M. Navara.

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Mesiarová-Zemánková, A. Sensitivity analysis of fuzzy rule-based classification systems by means of the Lipschitz condition. Soft Comput 20, 103–113 (2016). https://doi.org/10.1007/s00500-015-1744-z

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