Modelagem Quantum-Fuzzy XOR Fuzzy E⊖
Resumo
Este artigo apresenta a modelagem de operadores da Lógica Fuzzy via Computação Quântica, analisando o conectivo XOR que é obtido pela diferença entre a união e a intersecção entre conjuntos fuzzy, realizando ainda as evoluções considerando a instanciação dos dados de entrada.
Palavras-chave:
Lógica Fuzzy, operador XOR, construções Fuzzy-Quântico
Referências
Aboughalia, R. A. and Alkishriwo, O. A. S. (2018). Color Image Encryption Based on Chaotic Block Permutation and XOR Operation. http://doi.org/10.48550/arXiv.1808.10198
Acampora, G., Schiattarella, R., and Vitiello, A. (2023). On the Implementation of Fuzzy Inference Engines on Quantum Computers. IEEE Transactions on Fuzzy Systems, 31(5):1419-1433. http://doi.org/10.1145/1457199.145723510.1109/TFUZZ.2022.3202348.
Agostini, L. B., da Silva Feitosa, S., de Avila, A. B., Reiser, R., Dubois, A., and Pilla, M. L. (2018). Representing Intuistionistic Fuzzy Bi-implications Using Quantum Computing. In Guilherme A. Barreto and Ricardo Coelho, editor, Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Fortaleza, Brazil, July 4-6, 2018, Proceedings, volume 831 of Communications in Computer and Information Science, pages 206-216. Springer. http://doi.org/10.1007/978-3-319-95312-0_18
Bedregal, B. R. C., Reiser, R. H. S., and Dimuro, G. P. (2013a). Revisiting XOR-Implications: Classes of fuzzy (Co)Implications Based on F-XOR (F-XNOR) Connectives. Int. J. Uncertain. Fuzziness Knowl. Based Syst., 21(6):899-926. http://doi.org/10.1142/S0218488513500414
Bedregal, B. R. C., Reiser, R. H. S., and Dimuro, G. P. (2013b). Revisiting XOR-Implications: Classes of fuzzy (Co)Implications Based on F-XOR (F-XNOR) Connectives. Int. J. Uncertain. Fuzziness Knowl. Based Syst., 21(6):899-926. https://doi.org/10.1142/S0218488513500414
Cressman, A. J., Wattanapanitch, W., Chuang, I., and Sarpeshkar, R. (2022). Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits. Neural Comput., 34(4):856-890. https://doi.org/10.1162/neco_a_01481
de Avila, A. B., Santos, H. S., Cruz, A. P., de Souza, S. X., Lucca, G., Moura, B., Yamin, A. C., and Reiser, R. (2023). HybriD-GM: A Framework for Quantum Computing Simulation Targeted to Hybrid Parallel Architectures. Entropy, 25(3):503. http://doi.org/10.3390/e25030503
Dirac, P. A. M. (1939). A new notation for quantum mechanics. Mathematical Proceedings of the Cambridge Philosophical Society, 35(3):416-418. https://doi.org/10.1017/S0305004100021162
Klement, E. P. and Navara, M. (1999). Fuzzy Sets, Logics and Reasoning About Knowledge, volume 15 of Applied logics, chapter Propositional fuzzy logics based on Frank t-norms: A comparison, pages 17-38. Kluwer Academic Publishers, Dorbrech. https://doi.org/10.1007/978-94-017-1652-9_3
Mannucci, M. A. (2006). Quantum fuzzy sets: Blending fuzzy set theory and quantum computation. CoRR, abs/cs/0604064. https://doi.org/10.48550/arXiv.cs/0604064
Maron, A. K. (2010). Estendendo o vpe-qgm para suporte a simulações paralelas/distribuídas. Bacharelado em ciência da computação, Universidade Católica de Pelotas, Pelotas/RS.
Maron, A., Visintin, L., Reiser, R. H. S., and Abeijon, A. M. (2013). Fuzzy computing from quantum computing - case study in reichenbach implication class. Mathware & Soft Computing, 20(6):86-114.
Nielsen, M. A. and Chuang, I. L. (2011). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York, NY, USA, 10th edition. https://doi.org/10.1017/CBO9780511976667
Portugal, R., Lavor, C. C., Carvalho, L. M., and Maculan, N. (2004). Notas em Matemática aplicada 8. Sociedade Brasileira de Matemática Aplicada e Computacional, São Carlos/SP.
Sharma, M., Ranjan, R. K., and Bharti, V. (2022). A pseudo-random bit generator based on chaotic maps enhanced with a bit-XOR operation. Journal of Information Security and Applications, 69:103299. https://doi.org/10.1016/j.jisa.2022.103299
Acampora, G., Schiattarella, R., and Vitiello, A. (2023). On the Implementation of Fuzzy Inference Engines on Quantum Computers. IEEE Transactions on Fuzzy Systems, 31(5):1419-1433. http://doi.org/10.1145/1457199.145723510.1109/TFUZZ.2022.3202348.
Agostini, L. B., da Silva Feitosa, S., de Avila, A. B., Reiser, R., Dubois, A., and Pilla, M. L. (2018). Representing Intuistionistic Fuzzy Bi-implications Using Quantum Computing. In Guilherme A. Barreto and Ricardo Coelho, editor, Fuzzy Information Processing - 37th Conference of the North American Fuzzy Information Processing Society, NAFIPS 2018, Fortaleza, Brazil, July 4-6, 2018, Proceedings, volume 831 of Communications in Computer and Information Science, pages 206-216. Springer. http://doi.org/10.1007/978-3-319-95312-0_18
Bedregal, B. R. C., Reiser, R. H. S., and Dimuro, G. P. (2013a). Revisiting XOR-Implications: Classes of fuzzy (Co)Implications Based on F-XOR (F-XNOR) Connectives. Int. J. Uncertain. Fuzziness Knowl. Based Syst., 21(6):899-926. http://doi.org/10.1142/S0218488513500414
Bedregal, B. R. C., Reiser, R. H. S., and Dimuro, G. P. (2013b). Revisiting XOR-Implications: Classes of fuzzy (Co)Implications Based on F-XOR (F-XNOR) Connectives. Int. J. Uncertain. Fuzziness Knowl. Based Syst., 21(6):899-926. https://doi.org/10.1142/S0218488513500414
Cressman, A. J., Wattanapanitch, W., Chuang, I., and Sarpeshkar, R. (2022). Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits. Neural Comput., 34(4):856-890. https://doi.org/10.1162/neco_a_01481
de Avila, A. B., Santos, H. S., Cruz, A. P., de Souza, S. X., Lucca, G., Moura, B., Yamin, A. C., and Reiser, R. (2023). HybriD-GM: A Framework for Quantum Computing Simulation Targeted to Hybrid Parallel Architectures. Entropy, 25(3):503. http://doi.org/10.3390/e25030503
Dirac, P. A. M. (1939). A new notation for quantum mechanics. Mathematical Proceedings of the Cambridge Philosophical Society, 35(3):416-418. https://doi.org/10.1017/S0305004100021162
Klement, E. P. and Navara, M. (1999). Fuzzy Sets, Logics and Reasoning About Knowledge, volume 15 of Applied logics, chapter Propositional fuzzy logics based on Frank t-norms: A comparison, pages 17-38. Kluwer Academic Publishers, Dorbrech. https://doi.org/10.1007/978-94-017-1652-9_3
Mannucci, M. A. (2006). Quantum fuzzy sets: Blending fuzzy set theory and quantum computation. CoRR, abs/cs/0604064. https://doi.org/10.48550/arXiv.cs/0604064
Maron, A. K. (2010). Estendendo o vpe-qgm para suporte a simulações paralelas/distribuídas. Bacharelado em ciência da computação, Universidade Católica de Pelotas, Pelotas/RS.
Maron, A., Visintin, L., Reiser, R. H. S., and Abeijon, A. M. (2013). Fuzzy computing from quantum computing - case study in reichenbach implication class. Mathware & Soft Computing, 20(6):86-114.
Nielsen, M. A. and Chuang, I. L. (2011). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York, NY, USA, 10th edition. https://doi.org/10.1017/CBO9780511976667
Portugal, R., Lavor, C. C., Carvalho, L. M., and Maculan, N. (2004). Notas em Matemática aplicada 8. Sociedade Brasileira de Matemática Aplicada e Computacional, São Carlos/SP.
Sharma, M., Ranjan, R. K., and Bharti, V. (2022). A pseudo-random bit generator based on chaotic maps enhanced with a bit-XOR operation. Journal of Information Security and Applications, 69:103299. https://doi.org/10.1016/j.jisa.2022.103299
Publicado
09/10/2023
Como Citar
NOVACK, Bruna; BUSS, Juliano; SANTOS, Helida; LUCCA, Giancarlo; AVILA, Anderson; YAMIN, Adenauer; CRUZ, Anderson; REISER, Renata.
Modelagem Quantum-Fuzzy XOR Fuzzy E⊖. In: WORKSHOP-ESCOLA DE INFORMÁTICA TEÓRICA (WEIT), 7. , 2023, Rio Grande/RS.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2023
.
p. 62-70.
DOI: https://doi.org/10.5753/weit.2023.26598.
