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On the Additional Properties of Fuzzy Polynomial Implications of Degree 4

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

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Abstract

It is well known that fuzzy implication functions have a very flexible definition that encompasses lots of different potential families. Therefore, the additional properties that the family members fulfill define the behavior these operators will have when modeling fuzzy conditionals or applied to any other application. In this way, in this paper, we study the additional properties of fuzzy polynomial implications of degree 4, a recent family of fuzzy implications which has been recently introduced as a family whose members have a simple expression, appealing for applied researchers. It is proved that members of this family fulfill some of the additional essential properties of fuzzy implication functions.

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Notes

  1. 1.

    We refer the reader to [9] for more details on powers of continuous t-norms.

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Acknowledgements

This paper is part of the R+D+i Project PID2020-113870GB-I00- “Desarrollo de herramientas de Soft Computing para la Ayuda al Diagnóstico Clínico y a la Gestión de Emergencias (HESOCODICE)”, funded by MCIN/AEI/10.13039/501100011033/. Raquel Fernandez-Peralta benefits from the fellowship FPU18/05664 granted by the Spanish Ministry of Science, Innovation and Universities within the Training University Lecturers (FPU) program. The research activities co-financed by the funds granted under the Research Excellence Initiative of the University of Silesia in Katowice.

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Authors and Affiliations

  1. Faculty of Science and Technology, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński

  2. Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma, Balearic Islands, Spain

    Raquel Fernandez-Peralta, Sebastia Massanet, Arnau Mir & Juan Vicente Riera

  3. Health Research Institute of the Balearic Islands (IdISBa), 07010, Palma, Spain

    Raquel Fernandez-Peralta, Sebastia Massanet, Arnau Mir & Juan Vicente Riera

Authors
  1. Michał Baczyński
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  2. Raquel Fernandez-Peralta
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  3. Sebastia Massanet
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  4. Arnau Mir
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  5. Juan Vicente Riera
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Corresponding author

Correspondence to Sebastia Massanet .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Baczyński, M., Fernandez-Peralta, R., Massanet, S., Mir, A., Riera, J.V. (2022). On the Additional Properties of Fuzzy Polynomial Implications of Degree 4. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_16

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

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