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Two classes of ordinal sum implications

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Abstract

This article aims to contribute to the theory of ordinal sum implications by introducing two new classes: the minor ordinal sum implications and the major ordinal sum implications. The study presents diverse construction methods employed in generating examples of these two new classes. A method of constructing ordinal sums of implications that may be neither major nor minor is also presented. Furthermore, the article extends its contribution by providing examples of major and minor ordinal sum implications within some of the main classes of fuzzy implications, including (S,N)-implications, (T,N)-implications, QL-implications and D-implications. A study of the properties satisfied by the new ordinal sum implications is also presented.

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Author notes

  1. Landerson Santiago, Jocivania Pinheiro, Thadeu Milfont and Anne Canuto contributed equally to this work.

Authors and Affiliations

  1. Departamento de Ciência e Tecnologia, Universidade Federal Rural do Semi-Árido-UFERSA, Caraúbas, Rio Grande do Norte, 59780-000, Brazil

    Heloisa Frazao & Landerson Santiago

  2. Departamento de Informática e Matemática Aplicada-DIMAp, Universidade Federal do Rio Grande do Norte-UFRN, Natal, Rio Grande do Norte, 59078-970, Brazil

    Heloisa Frazao & Anne Canuto

  3. Departamento de Ciências Naturais, Matemática e Estatística, Universidade Federal Rural do Semi-Árido-UFERSA, Mossoró, Rio Grande do Norte, 59625-900, Brazil

    Jocivania Pinheiro & Thadeu Milfont

Authors
  1. Heloisa Frazao
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  2. Landerson Santiago
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  3. Jocivania Pinheiro
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  4. Thadeu Milfont
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  5. Anne Canuto
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Correspondence to Heloisa Frazao or Landerson Santiago.

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Frazao, H., Santiago, L., Pinheiro, J. et al. Two classes of ordinal sum implications. Comp. Appl. Math. 43, 220 (2024). https://doi.org/10.1007/s40314-024-02750-2

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  • DOI: https://doi.org/10.1007/s40314-024-02750-2

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