Geodesic
On type-2 fuzzy sets and type-2 fuzzy systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 114-122.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: fuzzy set of type 2, fuzzy relation of type 2, functional fuzzy system, relational fuzzy system. 
@article{INTO_2019_165_a9,
     author = {A. S. Shvedov},
     title = {On type-2 fuzzy sets and type-2 fuzzy systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {114--122},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a9/}
}
TY  - JOUR
AU  - A. S. Shvedov
TI  - On type-2 fuzzy sets and type-2 fuzzy systems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 114
EP  - 122
VL  - 165
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_165_a9/
LA  - ru
ID  - INTO_2019_165_a9
ER  - 
%0 Journal Article
%A A. S. Shvedov
%T On type-2 fuzzy sets and type-2 fuzzy systems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 114-122
%V 165
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_165_a9/
%G ru
%F INTO_2019_165_a9
A. S. Shvedov. On type-2 fuzzy sets and type-2 fuzzy systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 114-122. http://geodesic.mathdoc.fr/item/INTO_2019_165_a9/

[1] Lyu B., Teoriya i praktika neopredelennogo programmirovaniya, BINOM. Laboratoriya znanii, M., 2005

[2] Olizarenko S. A., Perepelitsa A. V., Kapranov V. A., “Nechetkie logicheskie sistemy intervalnogo tipa $2$. Arkhitektura i mekhanizm vyvoda”, Sist. obrobki inform., 2011, no. 5, 156–164

[3] Pegat A., Nechetkoe modelirovanie i upravlenie, BINOM. Laboratoriya znanii, M., 2013

[4] Rutkovskii L., Metody i tekhnologii iskusstvennogo intellekta, Goryachaya liniya — Telekom, M., 2010

[5] Shvedov A. S., “Nechetkoe matematicheskoe programmirovanie: kratkii obzor”, Probl. upravl., 2017, no. 3, 2–10

[6] Shvedov A. S., “Approksimatsiya funktsii s pomoschyu neironnykh setei i nechetkikh sistem”, Probl. upravl., 2018, no. 1, 21–29

[7] Castillo O., Melin P., Type-2 Fuzzy Logic: Theory and Applications, Springer-Verlag, Berlin, 2008 | Zbl

[8] Celik E., Gul M., Aydin N., Gumus A. T., Guneri A. F., “A comprehensive review of multi criteria decision making approaches based on interval type-2 fuzzy sets”, Knowledge-Based Syst., 85 (2015), 329–341 | DOI

[9] Chang P.-C., Liu C.-H., “A TSK type fuzzy rule based system for stock price prediction”, Expert Syst. Appl., 34 (2008), 135–144 | DOI

[10] Chang P.-C., Wu J.-L., Lin J.-J., “A Takagi–Sugeno fuzzy model combined with a support vector regression for stock trading forecasting”, Appl. Soft Comput., 38 (2016), 831–842 | DOI

[11] Du Z., Yan Z., Zhao Z., “Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller”, Fuzzy Sets Syst., 356 (2019), 92–112 | DOI | MR

[12] Hagras H., “A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots”, IEEE Trans. Fuzzy Syst., 12 (2004), 524–539 | DOI

[13] Hamza M. F., Yap H. J., Choudhury I. A., Chiroma H., Kumbasar T., “A survey on advancement of hybrid type 2 fuzzy sliding mode control”, Neural Comput. Appl., 30:2 (2018), 331–353 | DOI

[14] Hu B. Q., Wang C. Y., “On type-2 fuzzy relations and interval-valued type-2 fuzzy sets”, Fuzzy Sets Syst., 236 (2014), 1–32 | DOI | MR | Zbl

[15] John R. I., Coupland S., “Type-2 fuzzy logic: A historical view”, IEEE Comput. Intel. Mag., 2:1 (2007), 57–62 | DOI

[16] Karnik N. N., Mendel J. M., “Centroid of a type-2 fuzzy set”, Inform. Sci., 132 (2001), 195–220 | DOI | MR | Zbl

[17] Kumar A., Sharma S., Mitra R., “Design of type-2 fuzzy controller based on LQR mapped fusion function”, Int. J. Intel. Syst. Appl., 8 (2012), 18–29

[18] Mendel J. M., “Type-2 fuzzy sets and systems: An overview”, IEEE Comput. Intel. Mag., 2:1 (2007), 20–29 | DOI

[19] Mendel J. M., “Type-2 fuzzy sets as well as computing with words”, IEEE Comput. Intel. Mag., 2:1 (2019), 82–95 | DOI

[20] Mendel J. M., Hagras H., Tan W.-W., Melek W. W., Ying H., Introduction to type-2 fuzzy logic control. Theory and applications, Wiley, Hoboken (New Jersey), 2014 | MR | Zbl

[21] Mizumoto M., Tanaka K., “Some properties of fuzzy sets of type 2”, Inform. Control., 31 (1976), 312–340 | DOI | MR | Zbl

[22] Nieminen J., “On the algebraic structure of fuzzy sets of type 2”, Kybernetika., 13:4 (1977), 261–273 | MR | Zbl

[23] Tai K., El-Sayed A.-R., Biglarbegian M., Gonzalez C. I., Castillo O., Mahmud S., “Review of recent type-2 fuzzy controller applications”, Algorithms., 9 (2016), 1–19 | DOI | MR

[24] Tang X., Deng L., Yu J. Qu H., “Output feedback predictive control of interval type-2 T-S fuzzy systems with markovian packet losses”, IEEE Trans. Fuzzy Syst., 26 (2018), 2450–2459 | DOI

[25] Torshizi A. D., Zarandi M. H. F., Zakeri H., “On type-reduction of type-2 fuzzy sets: A review”, Appl. Soft Comput., 27 (2015), 614–627 | DOI

[26] Wagner C., Hagras H., “Toward general type-2 fuzzy logic systems based on zSlices”, IEEE Trans. Fuzzy Syst., 18:4 (2010), 637–660 | DOI

[27] Xiao B., Lam H. K., Yang X., Yu Y., Reu H., “Tracking control design of interval type-2 polynomial-fuzzy-model-based systems with time-varying delay”, Engrg. Appl. Art. Intel., 75 (2018), 76–87 | DOI | MR

[28] Zadeh L. A., “The concept of a linguistic variable and its application to approximate reasoning, I”, Inform. Sci., 8 (1975), 199–249 | DOI | MR | Zbl

[29] Zhang Z., Niu Y., “Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures”, Int. J. Syst. Sci., 49 (2018), 3169–3181 | DOI | MR

[30] Zhou H.-B., Garibaldi J. M., John R. I., Chiclana F., “On constructing parsimonious type-2 fuzzy logic systems via influential rule selection”, IEEE Trans. Fuzzy Syst., 17:4 (2009), 654–667 | DOI