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Fuzzy Boundary Weak Implications

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

Abstract

An extension of fuzzy implications and coimplications, called fuzzy boundary weak implications (shortly, fuzzy bw-implications), is introduced and discussed in this paper. Firstly, by weakening the boundary conditions of fuzzy implications and coimplications, we introduce the concept of fuzzy bw-implications. And then, we investigate some of their basic properties. Next, the concept of fuzzy pseudo-negations is introduced and the natural pseudo-negations of fuzzy bw-implications are investigated. Finally, the fuzzy bw-implications generated, respectively, by aggregation operators and generator functions are discussed in details. This work is motivated by the fact that in real applications there are used some operators which are not fuzzy implications. We hope that such an extension of fuzzy (co)implications can provide a certain theoretical foundation for the real applications.

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Acknowledgment

The work on this paper for Hua-Wen Liu was supported by the National Natural Science Foundation of China (No. 61573211). The work on this paper for Michał Baczyński was supported by the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Hua-Wen Liu

  2. Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński

Authors
  1. Hua-Wen Liu
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  2. Michał Baczyński
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Corresponding author

Correspondence to Hua-Wen Liu .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Liu, HW., Baczyński, M. (2018). Fuzzy Boundary Weak Implications. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_52

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_52

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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