Abstract
One of the advantages of systems based on fuzzy logic (fuzzy systems) is the possibility of a soft switch from one set of values of input parameters of the system to another, when different conclusions are drawn for different sets of these values. A fuzzy set of type 2 is a direct generalization of an ordinary fuzzy set. In this paper, we review some branches of the theory of type-2 fuzzy sets and the theory of type-2 fuzzy systems. We discuss operations on type-2 fuzzy sets, type-2 fuzzy relations, and the centroids of type-2 fuzzy sets and describe type-2 functional fuzzy systems and type-2 relational fuzzy systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Castillo and P. Melin, Type-2 Fuzzy Logic: Theory and Applications, Springer-Verlag, Berlin (2008).
E. Celik, M. Gul, N. Aydin, A. T. Gumus, and A. F. Guneri, “A comprehensive review of multi criteria decision making approaches based on interval type-2 fuzzy sets,” Knowledge-Based Syst., 85, 329–341 (2015).
P.-C. Chang and C.-H. Liu, “A TSK type fuzzy rule based system for stock price prediction,” Expert Syst. Appl., 34, 135–144 (2008).
P.-C. Chang, J.-L. Wu, and J.-J. Lin, “A Takagi–Sugeno fuzzy model combined with a support vector regression for stock trading forecasting,” Appl. Soft Comput., 38, 831–842 (2016).
Z. Du, Z. Yan, and Z. Zhao, “Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller,” Fuzzy Sets Syst., 356, 92–112 (2019).
H. Hagras, “A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots,” IEEE Trans. Fuzzy Syst., 12, 524–539 (2004).
M. F. Hamza, H. J. Yap, I. A. Choudhury, H. Chiroma, and T. Kumbasar, “A survey on advancement of hybrid type 2 fuzzy sliding mode control,” Neural Comput. Appl., 30, No. 2, 331–353 (2018).
B. Q. Hu and C. Y. Wang, “On type-2 fuzzy relations and interval-valued type-2 fuzzy sets,” Fuzzy Sets Syst., 236, 1–32 (2014).
R. I. John and S. Coupland, “Type-2 fuzzy logic: A historical view,” IEEE Comput. Intel. Mag., 2, No. 1, 57–62 (2007).
N. N. Karnik and J. M. Mendel, “Centroid of a type-2 fuzzy set,” Inform. Sci., 132, 195–220 (2001).
A. Kumar, S. Sharma, and R. Mitra, “Design of type-2 fuzzy controller based on LQR mapped fusion function,” Int. J. Intel. Syst. Appl., 8, 18–29 (2012).
B. Liu, Theory and Practice of Uncertain Programming, Physica-Verlag, Heidelberg (2002).
J. M. Mendel, “Type-2 fuzzy sets and systems: An overview,” IEEE Comput. Intel. Mag., 2, No. 1, 20–29 (2007).
J. M. Mendel, “Type-2 fuzzy sets as well as computing with words,” IEEE Comput. Intel. Mag., 2, No. 1, 82–95 (2019).
J. M. Mendel, H. Hagras, W.-W. Tan, W. W. Melek, and H. Ying, Introduction to type-2 fuzzy logic control. Theory and applications, Wiley, Hoboken (New Jersey) (2014).
M. Mizumoto and K. Tanaka, “Some properties of fuzzy sets of type 2,” Inform. Control., 31, 312–340 (1976).
J. Nieminen, “On the algebraic structure of fuzzy sets of type 2,” Kybernetika, 13, No. 4, 261–273 (1977).
S. A. Olizarenko, A. V. Perepelitca, and V. A. Kapranov, “The interval type-2 fuzzy logic system. The architecture and the inference engine,” Sist. Obrob. Inform., No. 5, 156–164 (2011).
A. Piegat, Fuzzy Modeling and Control, Physica-Verlag, Heidelberg (2001).
L. Rutkowski, Metody i Techniki Sztucznej Inteligencji, Wydawnictwo Naukowe PWN, Warszawa (2005).
A. S. Shvedov, “Fuzzy mathematical programming: A brief review,” Probl. Upravl., No. 3, 2–10 (2017).
A. S. Shvedov, “Functions approximating by neural networks and fuzzy systems,” Probl. Upravl., No. 1, 21–29 (2018).
K. Tai, A.-R. El-Sayed, M. Biglarbegian, C. I. Gonzalez, O. Castillo, and S. Mahmud, “Review of recent type-2 fuzzy controller applications,” Algorithms, 9, 1–19 (2016).
X. Tang, L. Deng, J. Yu, and H. Qu, “Output feedback predictive control of interval type-2 T-S fuzzy systems with markovian packet losses,” IEEE Trans. Fuzzy Syst., 26, 2450–2459 (2018).
A. D. Torshizi, M. H. F. Zarandi, and H. Zakeri, “On type-reduction of type-2 fuzzy sets: A review,” Appl. Soft Comput., 27, 614–627 (2015).
C. Wagner and H. Hagras, “Toward general type-2 fuzzy logic systems based on zSlices,” IEEE Trans. Fuzzy Syst., 18, No. 4, 637–660 (2010).
B. Xiao, H. K. Lam, X. Yang, Y. Yu, and H. Reu, “Tracking control design of interval type-2 polynomial-fuzzy-model-based systems with time-varying delay,” Engrg. Appl. Art. Intel., 75, 76–87 (2018).
L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning, I,” Inform. Sci., 8, 199–249 (1975).
Z. Zhang and Y. Niu, “Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures,” Int. J. Syst. Sci., 49, 3169–3181 (2018).
H.-B. Zhou, J. M. Garibaldi, R. I. John, and F. Chiclana, “On constructing parsimonious type-2 fuzzy logic systems via influential rule selection,” IEEE Trans. Fuzzy Syst., 17, No. 4, 654–667 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 165, Proceedings of the IV International Scientific Conference “Actual Problems of Applied Mathematics,” Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, 2019.
Rights and permissions
About this article
Cite this article
Shvedov, A.S. On Type-2 Fuzzy Sets and Type-2 Fuzzy Systems. J Math Sci 259, 376–384 (2021). https://doi.org/10.1007/s10958-021-05624-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-021-05624-8