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Implications Generated by Triples of Monotone Functions

  • Conference paper
Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

In this paper we deal with fuzzy implications generated via triples of monotone functions f,g,h. This idea has been presented for the first time at the IPMU 2012 conference, where we have introduced the generating formula and studied some special cases of these fuzzy implications. In our contribution we further develop this concept and study properties of generated fuzzy implications. More precisely,we study how some specific properties of generators f,g,h influence properties of the corresponding fuzzy implications.

We give also some examples of such generated fuzzy implications and examples illustrating the intersection of the system of fuzzy implications generated by this method with known types of generated fuzzy implications.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, FEEC Brno Uni. of Technology, Technická 8, Cz-616 00, Brno, Czech Republic

    Dana Hliněná

  2. Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology in Bratislava, Radlinského 11, Sk-813 68, Bratislava, Slovakia

    Martin Kalina

  3. Dept. of Quantitative Methods and Information Systems, Faculty of Economics, Matej Bel University, Tajovského 10, Sk-975 90, Banská Bystrica, Slovakia

    Pavol Král’

Authors
  1. Dana Hliněná
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  2. Martin Kalina
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  3. Pavol Král’
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Corresponding author

Correspondence to Dana Hliněná .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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Hliněná, D., Kalina, M., Král’, P. (2013). Implications Generated by Triples of Monotone Functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_42

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

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