Quantum-Fuzzy XOR Fuzzy E⊖ Modeling
Abstract
This article presents the modeling of Fuzzy Logic operators via Quantum Computing, analyzing the XOR connective that is obtained by the difference between the union and the intersection between fuzzy sets, also performing evo lutions considering the instantiation of the input data.
Keywords:
Fuzzy Logic, XOR operator, Fuzzy-Quantum constructions
References
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
Published
2023-10-09
How to Cite
NOVACK, Bruna; BUSS, Juliano; SANTOS, Helida; LUCCA, Giancarlo; AVILA, Anderson; YAMIN, Adenauer; CRUZ, Anderson; REISER, Renata.
Quantum-Fuzzy XOR Fuzzy E⊖ Modeling. In: WORKSHOP-SCHOOL ON THEORETICAL COMPUTER SCIENCE (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.
