Geração de Implicações Representáveis via Funções General-Overlap e General-Grouping
Resumo
As funções de implicação são geralmente geradas por agregadores que exigem propriedades como associatividade e elemento neutro. Este estudo preocupa-se com a flexibilização/substituição de algumas das principais propriedades analíticas de conectivos fuzzy, visando garantir a geração de novos operadores, como funções overlap e grouping, que flexibilizem condições e portanto estendam a abordagem de implicações fuzzy.
Palavras-chave:
Lógica Fuzzy, Funções Overlap, Funções Grouping, Implicações, Flexibilização de operadores
Referências
Baczyński, M. and Jayaram, B. (2008). (S, N)- and R-implications: A state-of-the-art survey. Fuzzy Sets Syst., 159(14):1836-1859. https://doi.org/10.1016/j.fss.2007.11.015
Baczyński, M. and Jayaram, B. (2010). QL-implications: Some properties and intersections. Fuzzy Sets Syst., 161:158-188. https://doi.org/10.1016/j.fss.2008.09.021
Bustince, H., Fernández, J., Mesiar, R., Montero, J., and Orduna, R. (2009). Overlap index, overlap functions and migrativity. In Carvalho, J. P., Dubois, D., Kaymak, U., and da Costa Sousa, J. M., editors, Proc. Joint 2009 Int. Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, pages 300-305.
Bustince, H., Fernandez, J., Mesiar, R., Montero, J., and Orduna, R. (2010). Overlap functions. Nonlinear Analysis: Theory, Methods & Applications, 72(3):1488-1499.
Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., and Herrera, F. (2012). Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Trans. on Fuzzy Systems, 20(3):405-415. http://doi.org/10.1109/TFUZZ.2011.2173581
DeMiguel, L., Gómez, D., Rodríguez, J. T., Montero, J., Bustince, H., Dimuro, G. P., and Sanz, J. A. (2019). General overlap functions. Fuzzy Sets Syst., 372:81-96. https://doi.org/10.1016/j.fss.2018.08.003
Dimuro, G. P., Bedregal, B., and Santiago, R. H. N. (2014). On (G,N)-implications derived from grouping functions. Information Sciences, 279:1-17. https://doi.org/10.1016/j.ins.2014.04.021
Dimuro, G. P., Bedregal, B., Bustince, H., Jurio, A., Baczynski, M., and Mis, K. (2017). QL-operations and QL-implication functions constructed from tuples (O, G, N) and the generation of fuzzy subsethood and entropy measures. Int. J. Approximate Reasoning, 82:170 - 192. https://doi.org/10.1016/j.ijar.2016.12.013
Dimuro, G. P., Santos, H. S., Bedregal, B. R. C., Borges, E. N., Palmeira, E. S., Fernández, J., and Bustince, H. (2019). On D-implications derived by grouping functions. In 2019 IEEE Intl Conf. on Fuzzy Systems, LA, USA, June 23-26, 2019, pages 1-6. IEEE. http://doi.org/10.1109/FUZZ-IEEE.2019.8858924
Fodor, J. C. (1995). Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems, 69(2):141-156
Gómez, D., Rodríguez, J. T., Montero, J., Bustince, H., and Barrenechea, E. (2016). n-Dimensional overlap functions. Fuzzy Sets Syst., 287:57-75. https://doi.org/10.1016/j.fss.2014.11.023
Klement, E. P. and Navara, M. (1999). A survey on different triangular norm-based fuzzy logics. Fuzzy Sets and Systems, 101(2):241-251. https://doi.org/10.1016/S0165-0114(98)00167-5
Mesiar, R. and Komornikova, M. (1997). Aggregation operators. Proc. XI Conference on applied Mathematics PRIM 96, pages 193-211.
Pekala, B. (2019). Uncertainty Data in Interval-Valued Fuzzy Set Theory - Properties, Algorithms and Applications, volume 367 of Studies in Fuzziness and Soft Computing. Springer. https://doi.org/10.1007/978-3-319-93910-0
Santos, H. S., Dimuro, G. P., da Cruz Asmus, T., Lucca, G., Borges, E. N., Bedregal, B. R. C., Sanz, J. A., Fernández, J., and Bustince, H. (2020). General grouping functions. In 18th Int. Conference, IPMU 2020, Lisbon, Portugal, Proceedings, Part II, volume 1238 of Com. in Computer and Inf. Science, pages 481-495. Springer. https://doi.org/10.1007/978-3-030-50143-3_38
Zadeh, L. A. (1965). Fuzzy sets. Inf. Control., 8(3):338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Baczyński, M. and Jayaram, B. (2010). QL-implications: Some properties and intersections. Fuzzy Sets Syst., 161:158-188. https://doi.org/10.1016/j.fss.2008.09.021
Bustince, H., Fernández, J., Mesiar, R., Montero, J., and Orduna, R. (2009). Overlap index, overlap functions and migrativity. In Carvalho, J. P., Dubois, D., Kaymak, U., and da Costa Sousa, J. M., editors, Proc. Joint 2009 Int. Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, pages 300-305.
Bustince, H., Fernandez, J., Mesiar, R., Montero, J., and Orduna, R. (2010). Overlap functions. Nonlinear Analysis: Theory, Methods & Applications, 72(3):1488-1499.
Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., and Herrera, F. (2012). Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Trans. on Fuzzy Systems, 20(3):405-415. http://doi.org/10.1109/TFUZZ.2011.2173581
DeMiguel, L., Gómez, D., Rodríguez, J. T., Montero, J., Bustince, H., Dimuro, G. P., and Sanz, J. A. (2019). General overlap functions. Fuzzy Sets Syst., 372:81-96. https://doi.org/10.1016/j.fss.2018.08.003
Dimuro, G. P., Bedregal, B., and Santiago, R. H. N. (2014). On (G,N)-implications derived from grouping functions. Information Sciences, 279:1-17. https://doi.org/10.1016/j.ins.2014.04.021
Dimuro, G. P., Bedregal, B., Bustince, H., Jurio, A., Baczynski, M., and Mis, K. (2017). QL-operations and QL-implication functions constructed from tuples (O, G, N) and the generation of fuzzy subsethood and entropy measures. Int. J. Approximate Reasoning, 82:170 - 192. https://doi.org/10.1016/j.ijar.2016.12.013
Dimuro, G. P., Santos, H. S., Bedregal, B. R. C., Borges, E. N., Palmeira, E. S., Fernández, J., and Bustince, H. (2019). On D-implications derived by grouping functions. In 2019 IEEE Intl Conf. on Fuzzy Systems, LA, USA, June 23-26, 2019, pages 1-6. IEEE. http://doi.org/10.1109/FUZZ-IEEE.2019.8858924
Fodor, J. C. (1995). Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems, 69(2):141-156
Gómez, D., Rodríguez, J. T., Montero, J., Bustince, H., and Barrenechea, E. (2016). n-Dimensional overlap functions. Fuzzy Sets Syst., 287:57-75. https://doi.org/10.1016/j.fss.2014.11.023
Klement, E. P. and Navara, M. (1999). A survey on different triangular norm-based fuzzy logics. Fuzzy Sets and Systems, 101(2):241-251. https://doi.org/10.1016/S0165-0114(98)00167-5
Mesiar, R. and Komornikova, M. (1997). Aggregation operators. Proc. XI Conference on applied Mathematics PRIM 96, pages 193-211.
Pekala, B. (2019). Uncertainty Data in Interval-Valued Fuzzy Set Theory - Properties, Algorithms and Applications, volume 367 of Studies in Fuzziness and Soft Computing. Springer. https://doi.org/10.1007/978-3-319-93910-0
Santos, H. S., Dimuro, G. P., da Cruz Asmus, T., Lucca, G., Borges, E. N., Bedregal, B. R. C., Sanz, J. A., Fernández, J., and Bustince, H. (2020). General grouping functions. In 18th Int. Conference, IPMU 2020, Lisbon, Portugal, Proceedings, Part II, volume 1238 of Com. in Computer and Inf. Science, pages 481-495. Springer. https://doi.org/10.1007/978-3-030-50143-3_38
Zadeh, L. A. (1965). Fuzzy sets. Inf. Control., 8(3):338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Publicado
09/10/2023
Como Citar
GALVÃO, Alessandra; SANTOS, Helida; LUCCA, Giancarlo; YAMIN, Adenauer; REISER, Renata.
Geração de Implicações Representáveis via Funções General-Overlap e General-Grouping. In: WORKSHOP-ESCOLA DE INFORMÁTICA TEÓRICA (WEIT), 7. , 2023, Rio Grande/RS.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2023
.
p. 29-36.
DOI: https://doi.org/10.5753/weit.2023.26594.
