UDC 516.813
|
|
2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 vlopanas@ukr.net
|
ALGEBRAIC OPERATIONS OVER FUZZY SETS AND RELATIONS IN AUTOMATA
INTERPRETATION WITH REALIZATION BY LOGICAL HARDWARE MEANS
Abstract. Algebraic operations over 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 substantiated.
Keywords: fuzzy sets, fuzzy relations, algebraic operations, finite automata, FPGA.
FULL TEXT
REFERENCES
- Kryvyi S.L., Opanasenko V.N., Zavyalov S.B. Logical operations over fuzzy sets and relations in automaton interpretation. Cybernetics and Systems Analysis. 2020. Vol. 56, N 6. P. 1012–1020. https://doi.org/10.1007/s10559-020-00321-x .
- Opanasenko V.N., Kryvyi S.L. Synthesis of neural-like networks on the basis of conversion of cyclic Hamming codes. Cybernetics and Systems Analysis. 2017. Vol. 53, N 4. P. 627–635. https://doi.org/10.1007/s10559-017-9965-z .
- Kryvyi S.L., Opanasenko V.M., Zavyalov S.B. Partitioning a set of vectors with integer coordinates by means of logical hardware. Cybernetics and Systems Analysis. 2019. Vol. 55, N 3. P. 462–473. https://doi.org/10.1007/s10559-019-00154-3.
- Kryvyi S.L., Opanasenko V.M. Partitioning a set of vectors with nonnegative integer coordinates using logical hardware. Cybernetics and Systems Analysis. 2018. Vol. 54, N 2. P. 310–319. https://doi.org/10.1007/s10559-018-0033-0.
- Kondratenko Y.P., Sidenko Ie.V. Decision-making based on fuzzy estimation of quality level for cargo delivery. Recent Developments and New Directions in Soft Computing. Studies in Fuzziness and Soft Computing. Cham: Springer, 2014. Vol. 317. P. 331–344. https://doi.org/ 10.1007/978-3-319-06323-2_21.
- Palagin A.V., Opanasenko V.N., Kryvyi S.L. Resource and energy optimization oriented development of FPGA-based adaptive logical networks for classification problem. Green IT Engineering: Components, Networks and Systems Implementation. Kharchenko V., Kondratenko Y., Kacprzyk J. (Eds.). 2017. Vol. 105. P. 195–218. https://doi.org/10.1007978 -3-319-55595-9_10.
- Borisov A.N., Alekseev A.V., Merkurieva G.V. Processing of fuzzy information in decision-making systems [in Russian]. Moscow: Radiosvyaz', 1989. 304 p.
- Palagin A., Opanasenko V. The implementation of extended arithmetics on FPGA-based structures. IEEE 9th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS 2017). Bucharest, Romania, 2017. Vol. 2. P. 1014–1019. https://doi.org/10.1109/IDAACS.2017.8095239.
- Kondratenko Y.P., Kondratenko N.Y. Soft computing analytic models for multiplication of asymmetrical fuzzy numbers. Recent Developments and the New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing. Cham: Springer, 2021. Vol. 393. P. 201–214. https://doi.org/10.1007/978-3-030-47124-8_17.
- Drozd J., Drozd O., Antoshchuk S., Kucshnerov A., Nikul V. Effectiveness of matrix and pipeline FPGA-based arithmetic components of safety-related systems. Proc. of 8th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems (IDAACS 2015) (24–26 Sept., 2015, Warsaw, Poland). 2015. Vol. 2. P. 785–789. https://doi.org/10.1109/IDAACS.2015.7341410.
- Bellman R., Zadeh L. Decision making in vague conditions. Problems of analysis and decision-making procedures. Moscow: Mir, 1976. P. 172–215.
- Kryvyi S.L. Introduction to methods of creating software products [in Ukrainian]. Kyiv: NaUKMA, 2018. 449 p.
