Conectivo Fuzzy XOR E⊗ - Interpretações Quantum-Fuzzy

• Juliano Buss Universidade Federal de Pelotas (UFPel) http://orcid.org/0009-0006-3862-5104
• Bruna Novack Universidade Federal de Pelotas (UFPel) https://orcid.org/0009-0001-2456-6282
• Helida Santos Universidade Federal do Rio Grande (FURG) http://orcid.org/0000-0003-2994-2862
• Giancarlo Lucca Universidade Católica de Pelotas (UCPel) http://orcid.org/0000-0002-3776-0260
• Anderson Avila Universidade Federal de Pelotas (UFPel) https://orcid.org/0000-0002-7275-0543
• Adenauer Yamin Universidade Federal de Pelotas (UFPel) http://orcid.org/0000-0002-7333-244X
• Anderson Cruz Universidade Federal do Rio Grande do Norte (UFRN) http://orcid.org/0000-0003-1505-352X
• Renata Reiser Universidade Federal de Pelotas (UFPel) http://orcid.org/0000-0001-9934-3115

DOI: https://doi.org/10.5753/weit.2023.26592

Resumo

Este artigo apresenta a modelagem de conectivos da Lógica Fuzzy utilizando a Computação Quântica, analisando a porta XOR, que se utiliza de ambos conectivos AND e OR para a sua construção, e apresentando a evolução dos estados na sua modelagem.

Palavras-chave: Computação Quântica, Lógica Fuzzy, operador XOR, construções Fuzzy-Quântico

Referências

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. https://doi.org/10.1007/978-3-319-95312-0_18

Aljafar, M. J., Perkowski, M. A., Acken, J. M., and Tan, R. (2018). A Time-Efficient CMOS-Memristive Programmable Circuit Realizing Logic Functions in Generalized AND-XOR Structures. IEEE Trans. Very Large Scale Integr. Syst., 26(1):23-36. https://doi.org/10.1109/TVLSI.2017.2750074

Aslan, M., Gunduz, M., and Kiran, M. S. (2019). JayaX: Jaya algorithm with xor operator for binary optimization. Applied Soft Computing, 82:105576. https://doi.org/10.1016/j.asoc.2019.105576

Bedregal, B. R. C., Reiser, R. H. S., and Dimuro, G. P. (2013). 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

Benini, L. C. and Jr Meneguette, M. (2009). UMA ABORDAGEM PARA MODELAGEM DE DADOS COM O USO DE SISTEMAS NEURO-FUZZY: APLICAÇÕES GEOESPACIAIS. Sociedade Brasileira de Matemática Aplicada e Computacional, São Carlos/SP.

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. https://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

Haaswijk, W., Soeken, M., Amarù, L. G., Gaillardon, P., and Micheli, G. D. (2017). A novel basis for logic rewriting. In 22nd Asia and South Pacific Design Automation Conference, ASP-DAC 2017, Chiba, Japan, January 16-19, 2017, pages 151-156.IEEE. https://doi.org/10.1109/ASPDAC.2017.7858312

Hocine, A., Kouaissah, N., and Lozza, S. O. (2023). XOR-analytic network process and assessing the impact of COVID-19 by sector. Computers Industrial Engineering, 177:109017. https://doi.org/10.1016/j.cie.2023.109017

Liu, F., Chen, Y., and Zhou, D. (2023). A two-dimensional approach to flexibility degree of XOR numbers with application to group decision making. Math. Comput. Simul., 207:267-287. https://doi.org/10.1016/j.matcom.2022.12.030

Mangal, M. and Singh, M. P. Analysis of Multidimensional Xor Classification Problem with Evolutionary Feedforward Neural Networks. Int. J. Artif. Intell. Tools, 16. https://doi.org/10.1142/S0218213007003229

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

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.

Wille, R., Chattopadhyay, A., and Drechsler, R. (2016). From reversible logic to quantum circuits: Logic design for an emerging technology. In Walid A. Najjar and Andreas Gerstlauer, editor, International Conference on Embedded Computer Systems: Architectures, Modeling and Simulation, SAMOS 2016, Agios Konstantinos, Samos Island, Greece, July 17-21, 2016, pages 268-274. IEEE. https://doi.org/10.1109/SAMOS.2016.7818357