Inference methods for fuzzy systems with non-singleton fuzzification
- Authors: Sinuk V.G.1, Kulabukhov S.V.1
-
Affiliations:
- Federal State Budget Educational Institution of Higher Education “Belgorod State Technological University named after V.G. Shukhov”
- Issue: No 2 (2023)
- Pages: 106-112
- Section: Mathematical foundations of information technology
- URL: https://journals.rcsi.science/2071-8632/article/view/286543
- DOI: https://doi.org/10.14357/20718632230211
- ID: 286543
Cite item
Abstract
The paper derives the inference result for widely used fuzzy systems in case of non-singleton fuzzification. It is achieved by means of the approach based on the fuzzy truth values, which made it possible to reduce the computational complexity of the inference down to polynomial and to generalize the conditions for logical inference. The most commonly used defuzzification methods in applications were considered along with the obtained expressions of inference result.
About the authors
V. G. Sinuk
Federal State Budget Educational Institution of Higher Education “Belgorod State Technological University named after V.G. Shukhov”
Email: vgsinuk@mail.ru
PhD, associate professor
Russian Federation, BelgorodS. V. Kulabukhov
Federal State Budget Educational Institution of Higher Education “Belgorod State Technological University named after V.G. Shukhov”
Author for correspondence.
Email: qlba@ya.ru
Postgraduate student
Russian Federation, BelgorodReferences
- Mamdani, E.: Applications of fuzzy algorithm for control a simple dynamic plant. Proc. IEEE 121(12), 1585–1588 (1974).
- Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man and Cybernetics 15(1), 116–132 (1985).
- Rutkowski, L.: Metody i tekhnologii iskusstvennogo intellekta [Computational Intelligence: Methods and Techniques]. Hot Line — Telecom, Moscow (2010)
- Pourabdollah, A., John, R., Garibaldi, J.M.: A new dynamic approach for non-singleton fuzzification in noisy time-series prediction. Proc. of FUZZ-IEEE 2017, pp. 1–6 (2017).
- Fu, C., Sarabakha, A., Kayacan, E., Wagner, C., John, R., Garibaldi, J.: Input uncertainty sensitivity enhanced nonsingleton fuzzy logic controllers for long-term navigation of quadrotor uavs. IEEE/ASME Transactions on Mechatronics 23(2), 725–734 (2018).
- Mendel, J.: Non-singleton fuzzification made simpler. Information Sciences 559, 286–308 (2021)
- Mendel, J.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions, second edn. Springer, Cham, Switzerland (2017).
- Mouzouris, G., Mendel, J.: Non-singleton fuzzy logic systems: Theory and application. IEEE Transactions on Fuzzy Systems 5(1), 56–71 (1997).
- Pegat, A.: Nechetkoe modelirovanie i upravlenie [Fuzzy Modelling and Control]. BINOM, Laboratory of Knowledge, Moscow (2009).
- Borisov, A., Krunberg, O., Fedorov, I.: Prinyatie reshenij na osnove nechetkih modelej [Decision Making Based on Fuzzy Models]. Zinatne, Riga (1990).
- Dubois, D., Prade, A.: Teoriya vozmozhnostej. Prilozhenie k predstavleniyu znanij v informatike [Possibility Theory. Application to Knowledge Representation in Computer Science]. Radio and Communication, Moscow (1990).
- Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics 3(1), 28–44 (1973).
- Sinuk, V., Mikhelev, V.: Metody vyvoda dlya sistem logicheskogo tipa na osnove nechetkoj stepeni istinnosti [Inference methods for logical systems based on fuzzy degree of truth]. Bulletin of Russian Academy of Scienc- es. Theory and Control Systems (3), 108–115 (2018).
- Sinuk, V.G., Polyakov, V.M., Kutsenko, D.A.: New fuzzy truth value based inference methods for non-singleton miso rule-based systems. Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI ’16) (2016)
- Dubois, D., Esteva, F., Godo, L., Prade, H.: Fuzzy-set Based Logics - An History-Oriented Presentation of Their Main Developments. In: M.D. Gabbay, W. John (eds.) The Many Valued and Nonmonotonic Turn in Logic, Handbook of the History of Logic book series, vol. 8, chap. 2.3 Fuzzy Truth-Values – Degree of Truth vs. Degree of Uncertainty, pp. 325–449. Elsevier (2007).
- Sugeno, M., Yasukawa, T.: A fuzzy-logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems 1, 7–31 (1993).
Supplementary files
