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The Origin of Fuzzy Extensions

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Springer Handbook of Computational Intelligence

Part of the book series: Springer Handbooks ((SHB))

Abstract

Many different kinds of sets have been defined within the framework of fuzzy sets . This paper focusses on those fuzzy set extensions that address the difficulties that experts find in order to build the membership values. In particular, we analyze type-2 fuzzy sets , interval-valued fuzzy sets , Atanassov’s intuitionistic fuzzy sets , or bipolar sets of type-2 and Atanassov’s interval-valued fuzzy sets. After stating a general approach to these extensions, we remark some structural problems in the extension problem and stress some applications for which the results obtained with extensions are better than those obtained with Zadeh’s fuzzy sets.

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Abbreviations

FDT:

fuzzy decision tree

FRBCS:

fuzzy rule-based classification systems

FURIA:

unordered fuzzy rule induction algorithm

GAGRAD:

genetic algorithm gradient

IF:

intuitionistic fuzzy

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Authors and Affiliations

  1. Dep. Automática y Computación, Universidad Pública de Navarra, 31006, Pamplona (Navarra), Spain

    Humberto Bustince, Edurne Barrenechea, Javier Fernández & Miguel Pagola

  2. Dep. Statistics and Operational Research, Complutense University, Madrid, Plaza de las Ciências, 3, 28040, Madrid, Spain

    Javier Montero

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  1. Humberto Bustince
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  2. Edurne Barrenechea
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  3. Javier Fernández
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  4. Miguel Pagola
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  5. Javier Montero
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Correspondence to Humberto Bustince .

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  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Bustince, H., Barrenechea, E., Fernández, J., Pagola, M., Montero, J. (2015). The Origin of Fuzzy Extensions. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_6

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