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Uniform Mixture Convergence of Continuously Transformed Fuzzy Systems

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Explainable AI and Other Applications of Fuzzy Techniques (NAFIPS 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 258))

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Abstract

The probability mixture structure of additive fuzzy systems allows uniform convergence of the generalized probability mixtures that represent the if-then rules of one system or of many combined systems. A new theorem extends this result and shows that it still holds uniformly for any continuous function of such fuzzy systems if the underlying functions are bounded. This allows fuzzy rule-based systems to approximate a far wider range of nonlinear behaviors for a given set of sample data and still produce an explainable probability mixture that governs the rule-based proxy system.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Bart Kosko

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  1. Bart Kosko
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Correspondence to Bart Kosko .

Editor information

Editors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Julia Rayz

  2. Purdue University, West Lafayette, IN, USA

    Victor Raskin

  3. University of Alberta, Edmonton, AB, Canada

    Scott Dick

  4. University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Kosko, B. (2022). Uniform Mixture Convergence of Continuously Transformed Fuzzy Systems. In: Rayz, J., Raskin, V., Dick, S., Kreinovich, V. (eds) Explainable AI and Other Applications of Fuzzy Techniques. NAFIPS 2021. Lecture Notes in Networks and Systems, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-82099-2_19

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