Choquet Fuzzy n-dimensional
Resumo
Na lógica fuzzy n-dimensional, o uso de graus adicionais e a ênfase na repetição de informações, juntamente com a integral de Choquet, tornam as decisões mais inteligentes e representativas. O objetivo deste estudo é estender a integral de Choquet fuzzy para a abordagem n-dimensional, explorando um novo campo de pesquisa e, assim, possibilitando o desenvolvimento e a expansão de novas técnicas de trabalho.
Palavras-chave:
Conjunto fuzzy n-dimensional, intervalos n-dimensionais, integral de Choquet, integral de Choquet n-dimensional
Referências
Bedregal, B., Beliakov, G., Bustince, H., Calvo, T., Fernández, J., and Mesiar, R. (2011). A characterization theorem for t-representable n-dimensional triangular norms. In Eurofuse 2011, pages 103–112. Springer. DOI: 10.1007/978-3-642-24001-0_11
Bedregal, B., Beliakov, G., Bustince, H., Calvo, T., Mesiar, R., and Paternain, D. (2012). A class of fuzzy multisets with a fixed number of memberships. Information Sciences, 189:1–17. DOI: 10.1016/j.ins.2011.11.040
Bedregal, B., Mezzomo, I., and Reiser, R. H. S. (2018). n-dimensional fuzzy negations. IEEE Transactions on Fuzzy Systems, 26(6):3660–3672. DOI: 10.1109/TFUZZ.2018.2842718
Beliakov, G., Pradera, A., Calvo, T., et al. (2007). Aggregation functions: A guide for practitioners, volume 221. Springer. DOI: 10.1007/978-3-540-73721-6
Beliakov, G., Sola, H. B., and Sánchez, T. C. (2016). A practical guide to averaging functions, volume 329. Springer. DOI: 10.1007/978-3-319-24753-3
Bottero, M., Ferretti, V., Figueira, J. R., Greco, S., and Roy, B. (2018). On the choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application. European Journal of Operational Research, 271(1):120–140. DOI: 10.1016/j.ejor.2018.04.022
Choquet, G. (1954). Theory of capacities: research on modern potential theory and Dirichlet problem, volume 5. University of Kansas, Department of Mathematics.
Dias, C. A., Bueno, J. C., Borges, E. N., Botelho, S. S., Dimuro, G. P., Lucca, G., Fernandéz, J., Bustince, H., and Drews Junior, P. L. J. (2018). Using the choquet integral in the pooling layer in deep learning networks. In North american fuzzy information processing society annual conference, pages 144–154. Springer. DOI: 10.1007/978-3-319-95312-0_13
Grabisch, M. (1996). The application of fuzzy integrals in multicriteria decision making. European journal of operational research, 89(3):445–456. DOI: 10.1016/0377-2217(95)00176-X
Lucca, G., Borges, E. N., Berri, R. A., Emmendorfer, L., Dimuro, G. P., and Asmus, T. C. (2021). On the generalizations of the choquet integral for application in frbcs. In Brazilian Conference on Intelligent Systems, pages 498–513. Springer. [link]
Lucca, G., Dimuro, G. P., Mattos, V., Bedregal, B., Bustince, H., and Sanz, J. A. (2015). A family of choquet-based non-associative aggregation functions for application in fuzzy rule-based classification systems. In 2015 IEEE international conference on fuzzy systems (FUZZ-IEEE), pages 1–8. IEEE. DOI: 10.1109/FUZZ-IEEE.2015.7337911
Pelegrina, G. D., Duarte, L. T., Grabisch, M., and Romano, J. M. T. (2020). The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification. European Journal of Operational Research, 282(3):945–956. DOI: 10.1016/j.ejor.2019.10.005
Scott, G. J., Marcum, R. A., Davis, C. H., and Nivin, T. W. (2017). Fusion of deep convolutional neural networks for land cover classification of high-resolution imagery. IEEE Geoscience and Remote Sensing Letters, 14(9):1638–1642. DOI: 10.1109/LGRS.2017.2722988
Shang, Y., Yuan, X., and Lee, E. (2010). The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets. Computers & Mathematics with Applications, 60(3):442 – 463. DOI: 10.1016/j.camwa.2010.04.044
Zanotelli, R., Reiser, R., and Bedregal, B. (2020). n-dimensional (s, n)-implications. International Journal of Approximate Reasoning, 126:1–26. DOI: 10.1016/j.ijar.2020.07.002
Zanotelli, R. M., Reiser, R. H. S., and Bedregal, B. R. C. (2021). n-dimensional fuzzy implications: analytical, algebraic and applicational approaches. In Workshop-Escola de Informática Teórica (WEIT), pages 171–178. SBC. DOI: 10.5753/weit.2021.18938
Bedregal, B., Beliakov, G., Bustince, H., Calvo, T., Mesiar, R., and Paternain, D. (2012). A class of fuzzy multisets with a fixed number of memberships. Information Sciences, 189:1–17. DOI: 10.1016/j.ins.2011.11.040
Bedregal, B., Mezzomo, I., and Reiser, R. H. S. (2018). n-dimensional fuzzy negations. IEEE Transactions on Fuzzy Systems, 26(6):3660–3672. DOI: 10.1109/TFUZZ.2018.2842718
Beliakov, G., Pradera, A., Calvo, T., et al. (2007). Aggregation functions: A guide for practitioners, volume 221. Springer. DOI: 10.1007/978-3-540-73721-6
Beliakov, G., Sola, H. B., and Sánchez, T. C. (2016). A practical guide to averaging functions, volume 329. Springer. DOI: 10.1007/978-3-319-24753-3
Bottero, M., Ferretti, V., Figueira, J. R., Greco, S., and Roy, B. (2018). On the choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application. European Journal of Operational Research, 271(1):120–140. DOI: 10.1016/j.ejor.2018.04.022
Choquet, G. (1954). Theory of capacities: research on modern potential theory and Dirichlet problem, volume 5. University of Kansas, Department of Mathematics.
Dias, C. A., Bueno, J. C., Borges, E. N., Botelho, S. S., Dimuro, G. P., Lucca, G., Fernandéz, J., Bustince, H., and Drews Junior, P. L. J. (2018). Using the choquet integral in the pooling layer in deep learning networks. In North american fuzzy information processing society annual conference, pages 144–154. Springer. DOI: 10.1007/978-3-319-95312-0_13
Grabisch, M. (1996). The application of fuzzy integrals in multicriteria decision making. European journal of operational research, 89(3):445–456. DOI: 10.1016/0377-2217(95)00176-X
Lucca, G., Borges, E. N., Berri, R. A., Emmendorfer, L., Dimuro, G. P., and Asmus, T. C. (2021). On the generalizations of the choquet integral for application in frbcs. In Brazilian Conference on Intelligent Systems, pages 498–513. Springer. [link]
Lucca, G., Dimuro, G. P., Mattos, V., Bedregal, B., Bustince, H., and Sanz, J. A. (2015). A family of choquet-based non-associative aggregation functions for application in fuzzy rule-based classification systems. In 2015 IEEE international conference on fuzzy systems (FUZZ-IEEE), pages 1–8. IEEE. DOI: 10.1109/FUZZ-IEEE.2015.7337911
Pelegrina, G. D., Duarte, L. T., Grabisch, M., and Romano, J. M. T. (2020). The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification. European Journal of Operational Research, 282(3):945–956. DOI: 10.1016/j.ejor.2019.10.005
Scott, G. J., Marcum, R. A., Davis, C. H., and Nivin, T. W. (2017). Fusion of deep convolutional neural networks for land cover classification of high-resolution imagery. IEEE Geoscience and Remote Sensing Letters, 14(9):1638–1642. DOI: 10.1109/LGRS.2017.2722988
Shang, Y., Yuan, X., and Lee, E. (2010). The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets. Computers & Mathematics with Applications, 60(3):442 – 463. DOI: 10.1016/j.camwa.2010.04.044
Zanotelli, R., Reiser, R., and Bedregal, B. (2020). n-dimensional (s, n)-implications. International Journal of Approximate Reasoning, 126:1–26. DOI: 10.1016/j.ijar.2020.07.002
Zanotelli, R. M., Reiser, R. H. S., and Bedregal, B. R. C. (2021). n-dimensional fuzzy implications: analytical, algebraic and applicational approaches. In Workshop-Escola de Informática Teórica (WEIT), pages 171–178. SBC. DOI: 10.5753/weit.2021.18938
Publicado
10/09/2025
Como Citar
ZANOTELLI, Rosana; DIMURO, Graçaliz.
Choquet Fuzzy n-dimensional. In: WORKSHOP-ESCOLA DE INFORMÁTICA TEÓRICA (WEIT), 8. , 2025, Ponta Grossa/PR.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2025
.
p. 178-183.
