×

zbMATH — the first resource for mathematics

On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. (English) Zbl 1227.93063
Summary: Research on the robustness of Fuzzy Logic Systems (FLSs), an imperative factor in the design process, is very limited in the literature. Specifically, when a system is subjected to small deviations of the sampling points (operating points), it is of great interest to find the maximum tolerance of the system, which we refer to as the system’s robustness. In this paper, we present a methodology for the robustness analysis of Interval Type-2 FLSs (IT2 FLSs) that also holds for T1 FLSs, hence, making it more general. A procedure for the design of robust IT2 FLSs with a guaranteed performance better than or equal to their T1 counterparts is then proposed. Several examples are performed to demonstrate the effectiveness of the proposed methodologies. It was concluded that both T1 and IT2 FLSs can be designed to achieve robust behavior in various applications, and preference one or the other, in general, is application-dependant. IT2 FLSs, having a more flexible structure than T1 FLSs, exhibited relatively small approximation errors in the several examples investigated. The methodologies presented in this paper lay the foundation for the design of FLSs with robust properties that will be very useful in many practical modeling and control applications.

MSC:
93C42 Fuzzy control/observation systems
93C95 Application models in control theory
Software:
GP-COACH
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Batanovica, V.; Petrovicb, D.; Petrovic, R., Fuzzy logicnext term based algorithms for maximum covering location problems, Information sciences, 179, 1-2, 120-129, (2009)
[2] Berlanga, F.J.; Rivera, A.J.; del Jesus, M.J.; Herrera, F., GP-COACH: genetic programming-based learning of compact and accurate fuzzy rule-based classification systems for high-dimensional problems, Information sciences, 180, 8, 1183-1200, (2010)
[3] Biglarbegian, M.; Melek, W.W.; Mendel, J.M., On the stability of interval type-2 TSK fuzzy logic control systems, IEEE transactions on systems, man, cybernetics: part B, 4, 3, 798-818, (2010)
[4] Cai, K.-Y., Robustness of fuzzy reasoning and δ-equalities of fuzzy sets, IEEE transactions on fuzzy systems, 9, 5, 738-750, (2001)
[5] Deschrijver, G., Arithmetic operators in interval-valued fuzzy set theory, Information sciences, 177, 14, 2906-2924, (2007) · Zbl 1120.03033
[6] Deschrijver, G.; Krl’, P., On the cardinalities of interval-valued fuzzy sets, Fuzzy sets and systems, 158, 15, 1728-1750, (2007) · Zbl 1120.03034
[7] Feng, G., A survey on analysis and design of model-based fuzzy control systems, IEEE transactions on fuzzy systems, 14, 5, 676-697, (2006)
[8] Gorlzakczany, M.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987)
[9] Barrenechea, E.; Bustince, H.; Pagola, M., Generation of interval-valued fuzzy and atanassov’s institutionistic fuzzy connectives and from k-alpha operators: laws for conjunctions and disjunctions, amplitude, International journal of intelligent systems, 23, 6, 680-714, (2008) · Zbl 1140.68499
[10] Hung, J.-C., A fuzzy asymmetric GARCH model applied to stock markets, Information sciences, 179, 22, 3930-3943, (2009)
[11] Li, Y.; Li, D.; Pedrycz, W.; Wu, J., An approach to measure the robustness of fuzzy reasoning, International journal of intelligent systems, 20, 4, 393-413, (2005) · Zbl 1101.68880
[12] Li, Y.; Li, D.; Pedrycz, W.; Wu, J., Approximation and robustness of fuzzy finite automata, International journal of approximate reasoning, 47, 2, 247-257, (2008) · Zbl 1184.68319
[13] Melek, W.W.; Goldenberg, A.A., The development of a robust fuzzy inference mechanism, International journal of approximate reasoning, 39, 1, 29-47, (2005) · Zbl 1065.68095
[14] Mendel, J.M., Uncertain rule-based fuzzy logic systems: introduction and new directions, (2001), Prentice-Hall Upper Saddle River, NJ · Zbl 0978.03019
[15] Mendel, J.M., Comments on α-plane representation for type-2 fuzzy sets: theory and applications, IEEE transactions on fuzzy systems, 18, 1, 229-230, (2010)
[16] Mendel, J.M.; Liu, F.; Zhai, D., α-plane representation for type-2 fuzzy sets: theory and applications, IEEE transactions on fuzzy systems, 17, 5, 1189-1207, (2009)
[17] Mendel, J.M.; Wu, D., Perceptual computing: aiding people in making subjective judgments, (2010), John Wiley & IEEE Press
[18] Mendel, Jerry M., On answering the question where do I start in order to solve a new problem involving interval type-2 fuzzy sets?, Information sciences, 179, 19, 3418-3431, (2009) · Zbl 1193.68249
[19] Mendez, G.M.; Hernandez, M.D.L.A., Hybrid learning for interval type-2 fuzzy logicnext term systems based on orthogonal least-squares and back-propagation method, Information sciences, 179, 13, 2146-2157, (2009)
[20] H.T. Nguyen, V. Kreinovich, D. Tolbert, On robustness of fuzzy logics, in: Second IEEE International Conference on Fuzzy Systems, Reno, NV, March-April 1993, pp. 543-547.
[21] Ozkana, I.; Erdena, L.; Turksen, I.B., A fuzzy analysis of country-size argument for the feldsteinhorioka puzzle, Information sciences, 179, 16, 2754-2761, (2009)
[22] Tanaka, K.; Yoshida, H.; Ohtake, H.; Wang, H.O., A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems, IEEE transactions on fuzzy systems, 17, 4, 911-922, (2009)
[23] Wang, L.-X., Adaptive fuzzy systems and control: design and stability analysis, (1994), Prentice-Hall NJ
[24] Ying, H., Fuzzy control and modeling: analytical foundations and applications, (2000), IEEE Press
[25] H. Ying, General interval type-2 Mamdani fuzzy systems are universal approximators, in: Proceedings of North American Fuzzy Information Processing Society (NAFIPS), New York City, USA, May 2008, pp. 1-6.
[26] H. Ying, Interval type-2 Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators, in: Proceedings of North American Fuzzy Information Processing Society (NAFIPS), Cincinnati, Ohio, USA, June 2009.
[27] Ying, M.S., Perturbation of fuzzy reasoning, IEEE transactions on fuzzy systems, 7, 5, 625-629, (1999)
[28] Zadeh, L.A., Is there a need for fuzzy logic?, Information sciences, 178, 13, 2751-2779, (2008) · Zbl 1148.68047
[29] Fazel Zarandi, M.H.; Alaeddini, A., A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts, Information sciences, 180, 16, 3033-3044, (2010)
[30] Zhang, Z.; Cai, K.-Y., Optimal fuzzy reasoning and its robustness analysis, International journal of intelligent systems, 19, 11, 1033-1049, (2004) · Zbl 1101.68889
[31] Z. Zheng, W. Liu, K.-Y. Cai. Robustness of fuzzy operators in environments with random perturbations, Journal of Soft Computing - A Fusion of Foundations, Methodologies and Applications, in press. Online available at: <http://www.springerlink.com/content/gl2m754583t65j43>.
[32] Zhou, S.-M.; John, R.I.; Chiclana, F.; Garibaldi, J.M., On aggregating uncertain information by type-2 OWA operators for soft decision making, International journal of intelligent systems, 25, 6, 540-558, (2010) · Zbl 1192.68691
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.