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An Overview of Construction Methods of Fuzzy Implications

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Advances in Fuzzy Implication Functions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 300))

Abstract

Fuzzy implications are useful in a wide range of applications. For these practical purposes, different classes of implications are used. Depending on the concrete application the implication is going to perform, several additional properties have to be fulfilled. In this paper, we recall briefly the most used classes of implications, (S,N) and R-implications, QL and D-operations, their generalizations to other aggregation functions and Yager’s implications, and we show the new construction methods presented in recent years. These construction methods vary from implications defined from general aggregation functions or fuzzy negations, to implications generated from one or two initial implications. For every single class, we determine which additional properties are satisfied.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa Km. 7.5, E-07122, Palma de Mallorca, Spain

    Sebastià Massanet & Joan Torrens

Authors
  1. Sebastià Massanet
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  2. Joan Torrens
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Correspondence to Sebastià Massanet .

Editor information

Editors and Affiliations

  1. , Institute of Mathematics, University of Silesia, ul. Bankowa 14, Katowice, 40-007, Poland

    Michał Baczyński

  2. School of Information Technology, Deakin University, Burwood Highway 221, Burwood, 3125, Victoria, Australia

    Gleb Beliakov

  3. Departamento de Automática y, Computación, Universidad Pública de Navarra, Campus Arrosadia Campus s/n, Pamplona, 31006, Spain

    Humberto Bustince Sola

  4. , Departamento de Ciencias de la, Universidad Rey Juan Carlos, c/ Tulipan s/n, Mostoles, 28933, Spain

    Ana Pradera

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Massanet, S., Torrens, J. (2013). An Overview of Construction Methods of Fuzzy Implications. In: Baczyński, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds) Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35677-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-35677-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35676-6

  • Online ISBN: 978-3-642-35677-3

  • eBook Packages: EngineeringEngineering (R0)

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