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Additive Fuzzy Systems as Generalized Probability Mixture Models

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Book cover Fifty Years of Fuzzy Logic and its Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

Abstract

Additive fuzzy systems generalize the popular mixture-density models of machine learning. Additive fuzzy systems map inputs to outputs by summing fired then-parts sets and then taking the centroid of the sum. This additive structure produces a simple convex structure: Outputs are convex combinations of the centroids of the fired then-part sets. Additive systems are uniform function approximators and admit simple learning laws that grow and tune rules from sample data. They also behave as conditional expectations with conditional variances and other higher moment that describe their uncertainty. But they suffer from exponential rule explosion in high dimensions. Extending finite-rule additive systems to fuzzy systems with continuum-many rules overcomes the problem of rule explosion if a higher-level mixture structure acts as a system of tunable meta-rules. Monte Carlo sampling can then compute fuzzy-system outputs.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Signal and Image Processing Institute, 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 .

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Editors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

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Kosko, B. (2015). Additive Fuzzy Systems as Generalized Probability Mixture Models. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_14

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19682-4

  • Online ISBN: 978-3-319-19683-1

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