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Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders

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Abstract

The interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets can be extended to a more general framework to simultaneously deal with uncertainty in both membership and non-membership values. This fact leads to the concept of interval-valued Atanassov intuitionistic fuzzy sets (IVAIFS), as given by Atanassov and Gargov (Fuzzy Sets Syst, 31(3):343–349, 1989). In this paper, we focus on the study of interval-valued Atanassov intuitionistic t-norms and t-conorms, studying important properties and characterizations of some of their sub-classes. In addition, we do not only consider just the usual order on IVAIFS, but also admissible orders. Finally, we establish the basis for the use of this study in the approximate reasoning context.

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Acknowledgements

This work was supported by the Brazilian funding agency CNPq (Brazilian Research Council) under Projects 301618/2019-4 and 311429/2020-3, FAPERGS (19/2551-0001660) and by the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB I00 (MCIN/AEI/10.13039/501100011033)).

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  1. Lucelia Lima, Marcus Rocha, Graçaliz Dimuro, Humberto Bustince have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Campus Universitário - Lagoa Nova, Natal, 59078-970, RN, Brazil

    Benjamín Bedregal

  2. Campus Ananindeua, Universidade da Amazônia, Rod. Bernardo Sayão, 8420 - Coqueiro, Ananindeua, 67030-007, PA, Brazil

    Lucelia Lima

  3. Faculdade de Matemática, Universidade Federal do Pará, R. Augusto Corrêa, 01 - Guamá, Belém, PA, 66075-110, Brazil

    Marcus Rocha

  4. Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Av. Itália, s/n - km 8 - Carreiros, Rio Grande, RS, 96203-900, Brazil

    Graçaliz Dimuro

  5. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Campus de Arrosadia, Pamplona, Navarra, 31006, Spain

    Graçaliz Dimuro & Humberto Bustince

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  1. Benjamín Bedregal
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  2. Lucelia Lima
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Correspondence to Benjamín Bedregal.

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Communicated by Regivan Hugo Nunes Santiago.

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Bedregal, B., Lima, L., Rocha, M. et al. Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders. Comp. Appl. Math. 42, 49 (2023). https://doi.org/10.1007/s40314-022-02179-5

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