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Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized ( h , e )-Implications

Author

Listed:
  • Raquel Fernandez-Peralta

    (Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
    Health Research Institute of the Balearic Islands (IdISBa), 07010 Palma, Spain)

  • Sebastia Massanet

    (Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
    Health Research Institute of the Balearic Islands (IdISBa), 07010 Palma, Spain)

  • Arnau Mir

    (Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
    Health Research Institute of the Balearic Islands (IdISBa), 07010 Palma, Spain)

Abstract

In this study, we analyze the family of generalized ( h , e ) -implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized ( h , e ) -implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the ( f , g ) and ( g , f ) -implications, which are two families of fuzzy implication functions that generalize the well-known f and g -generated implications proposed by Yager through a generalization of the internal factors x and 1 x , respectively. The behavior and additional properties of these two families are also studied in detail.

Suggested Citation

  • Raquel Fernandez-Peralta & Sebastia Massanet & Arnau Mir, 2021. "Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized ( h , e )-Implications," Mathematics, MDPI, vol. 9(13), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1490-:d:581718
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