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International Summer School on Aggregation Operators

AGOP 2017: Aggregation Functions in Theory and in Practice pp 253–262Cite as

Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

Abstract

The purpose of this paper is to study fuzzy operators induced by fuzzy relations and fuzzy relations induced by fuzzy operators. Many results are obtained about the relationship between \(*\)-preorders and fuzzy consequences operators for a fixed t-norm \(*\). We analyse these properties by considering a semi-copula (generalization of t-norm concept) instead of a t-norm. Moreover, we show that the conditions imposed cannot be relaxed. We have been able to prove some important results about the relationships between fuzzy relations and fuzzy operators in this more general context.

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Acknowledgements

The authors acknowledge the financial support of the Spanish Ministerio de Economía y Competitividad (Grant TIN2014-59543-P and Grant MTM 2016-79422-P) and Carlos Bejines also thanks the support of the Asociación de Amigos of the University of Navarra.

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Authors and Affiliations

  1. Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, Pamplona, Spain

    Carlos Bejines, María Jesús Chasco & Jorge Elorza

  2. Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain

    Susana Montes

Authors
  1. Carlos Bejines
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  2. María Jesús Chasco
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  3. Jorge Elorza
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  4. Susana Montes
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Corresponding author

Correspondence to Susana Montes .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Bejines, C., Chasco, M.J., Elorza, J., Montes, S. (2018). Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_26

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

  • eBook Packages: EngineeringEngineering (R0)

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