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Fuzzy Modifiers at the Core of Interpretable Fuzzy Systems

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Fifty Years of Fuzzy Logic and its Applications

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

Abstract

Fuzzy modifiers associated with linguistic hedges have been introduced by L.A. Zadeh at the early stage of approximate reasoning and they are fundamental elements in the management of interpretable systems. They can be regarded as a solution to the construction of fuzzy sets slightly different from original ones. We first present the main definitions of modifiers based on mathematical transformations of membership functions, mainly focusing on so-called post-modifiers and pre-modifiers, as well as definitions based on fuzzy relations. We show that measures of similarity are useful to evaluate the proximity between the original fuzzy sets and their modified form and we point out links between modifiers and similarities. We then propose an overview of application domains which can take advantage of fuzzy modifiers, for instance analogy-based reasoning, rule-based systems, gradual systems, databases, machine learning, image processing, and description logic. It can be observed that fuzzy modifiers are either constructed in a prior way by means of formal definitions or automatically learnt or tuned, for instance in hybrid systems involving genetic algorithm-based methods.

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Author information

Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, 75005, Paris, France

    Bernadette Bouchon-Meunier & Christophe Marsala

  2. CNRS, UMR 7606, LIP6, 75005, Paris, France

    Bernadette Bouchon-Meunier & Christophe Marsala

Authors
  1. Bernadette Bouchon-Meunier
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  2. Christophe Marsala
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Correspondence to Bernadette Bouchon-Meunier .

Editor information

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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Bouchon-Meunier, B., Marsala, C. (2015). Fuzzy Modifiers at the Core of Interpretable Fuzzy Systems. 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_4

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_4

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-19683-1

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