Algebraic Operations on Fuzzy Sets and Relations in Automata Interpretation Implemented by Logical Hardware
Tóm tắt
Algebraic operations on fuzzy sets and relations and their implementation by hardware in automata interpretation are considered. Two ways of representing the values of membership functions of fuzzy sets and methods of transformation of such images are described. Appropriate estimates of the complexity of operations with such images are given and correctness of the algorithms is proved.
Tài liệu tham khảo
S. L. Kryvyi, V. N. Opanasenko, and S. B. Zavyalov, “Logical operations over fuzzy sets and relations in automaton interpretation,” Cybern. Syst. Analysis, Vol. 56, No. 6, 1012–1020 (2020). https://doi.org/10.1007/s10559-020-00321-x.
V. N. Opanasenko and S. L. Kryvyi, “Synthesis of neural-like networks on the basis of conversion of cyclic Hamming codes,” Cybern. Syst. Analysis, Vol. 53, No. 4, 627–635 (2017). https://doi.org/10.1007/s10559-017-9965-z.
S. L. Kryvyi, V. M. Opanasenko, and S. B. Zavyalov, “Partitioning a set of vectors with integer coordinates by means of logical hardware,” Cybern. Syst. Analysis, Vol. 55, No. 3, 462–473 (2019). https://doi.org/10.1007/s10559-019-00154-3.
S. L. Kryvyi and V. M. Opanasenko, “Partitioning a set of vectors with nonnegative integer coordinates using logical hardware,” Cybern. Syst. Analysis, Vol. 54, No. 2, 310–319 (2018). https://doi.org/10.1007/s10559-018-0033-0.
Y. P. Kondratenko and Ie. V. Sidenko, “Decision-making based on fuzzy estimation of quality level for cargo delivery,” in: Recent Developments and New Directions in Soft Computing. Studies in Fuzziness and Soft Computing, Vol. 317, Springer, Cham (2014), pp. 331–344. https://doi.org/10.1007/978-3-319-06323-2_21.
A. V. Palagin, V. N. Opanasenko, and S. L. Kryvyi, “Resource and energy optimization oriented development of FPGA-based adaptive logical networks for classification problem,” in: V. Kharchenko, Y. Kondratenko, and J. Kacprzyk (eds.), Green IT Engineering: Components, Networks and Systems Implementation, Vol. 105 (2017), pp. 195–218. https://doi.org/10.1007/978-3-319-55595-9_10.
A. N. Borisov, A. V. Alekseev, and G. V. Merkur’eva, Processing of Fuzzy Information in Decision-Making Systems [in Russian], Radio i Svyaz’, Moscow (1989).
A. Palagin and V. Opanasenko, “The implementation of extended arithmetics on FPGA-based structures,” in: Proc. IEEE 9th Intern. Conf. on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS 2017), Vol. 2, Bucharest, Romania (2017), pp. 1014–1019. https://doi.org/10.1109/IDAACS.2017.8095239.
Y. P. Kondratenko and N. Y. Kondratenko, “Soft computing analytic models for multiplication of asymmetrical fuzzy numbers,” in: Recent Developments and the New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing, Vol. 393, Springer, Cham (2021), pp. 201–214. https://doi.org/10.1007/978-3-030-47124-8_17.
J. Drozd, O. Drozd, S. Antoshchuk, A. Kucshnerov, and V. Nikul, “Effectiveness of matrix and pipeline FPGA-based arithmetic components of safety-related systems,” in: Proc. 8th IEEE Intern. Conf. on Intelligent Data Acquisition and Advanced Computing Systems (IDAACS 2015) (Warsaw, Poland, 24–26 Sept, 2015), Vol. 2 (2015), pp. 785–789. https://doi.org/10.1109/IDAACS.2015.7341410.
R. Bellman and L. Zadeh, Decision-Making under Fuzzy Conditions. Analysis and Decision-Making Procedures [Russian translation], Mir, Moscow (1976), pp. 172–215.
S. L. Kryvyi, An Introduction to the Methods of Creating Software Products [in Ukrainian], NaUKMA, Kyiv (2018).