zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

93C42Fuzzy control systems
93C95Applications of control theory
Full Text: DOI
[1] Batanovica, V.; Petrovicb, D.; Petrovic, R.: Fuzzy logicnext term based algorithms for maximum covering location problems, Information sciences 179, No. 1 -- 2, 120-129 (2009) · Zbl 1156.90449 · doi:10.1016/j.ins.2008.08.019
[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, No. 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, No. 3, 798-818 (2010)
[4] Cai, K. -Y.: Robustness of fuzzy reasoning and $\delta $-equalities of fuzzy sets, IEEE transactions on fuzzy systems 9, No. 5, 738-750 (2001)
[5] Deschrijver, G.: Arithmetic operators in interval-valued fuzzy set theory, Information sciences 177, No. 14, 2906-2924 (2007) · Zbl 1120.03033 · doi:10.1016/j.ins.2007.02.003
[6] Deschrijver, G.; Krl’, P.: On the cardinalities of interval-valued fuzzy sets, Fuzzy sets and systems 158, No. 15, 1728-1750 (2007) · Zbl 1120.03034 · doi:10.1016/j.fss.2007.01.005
[7] Feng, G.: A survey on analysis and design of model-based fuzzy control systems, IEEE transactions on fuzzy systems 14, No. 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) · Zbl 0635.68103 · doi:10.1016/0165-0114(87)90148-5
[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, No. 6, 680-714 (2008) · Zbl 1140.68499 · doi:10.1002/int.20292
[10] Hung, J. -C.: A fuzzy asymmetric GARCH model applied to stock markets, Information sciences 179, No. 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, No. 4, 393-413 (2005) · Zbl 1101.68880 · doi:10.1002/int.20072
[12] Li, Y.; Li, D.; Pedrycz, W.; Wu, J.: Approximation and robustness of fuzzy finite automata, International journal of approximate reasoning 47, No. 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, No. 1, 29-47 (2005) · Zbl 1065.68095 · doi:10.1016/j.ijar.2004.08.003
[14] Mendel, J. M.: Uncertain rule-based fuzzy logic systems: introduction and new directions, (2001) · Zbl 0978.03019
[15] Mendel, J. M.: Comments on $\alpha $-plane representation for type-2 fuzzy sets: theory and applications, IEEE transactions on fuzzy systems 18, No. 1, 229-230 (2010)
[16] Mendel, J. M.; Liu, F.; Zhai, D.: $\alpha $-plane representation for type-2 fuzzy sets: theory and applications, IEEE transactions on fuzzy systems 17, No. 5, 1189-1207 (2009)
[17] Mendel, J. M.; Wu, D.: Perceptual computing: aiding people in making subjective judgments, (2010)
[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, No. 19, 3418-3431 (2009) · Zbl 1193.68249 · doi:10.1016/j.ins.2009.05.008
[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, No. 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, No. 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, No. 4, 911-922 (2009)
[23] Wang, L. -X.: Adaptive fuzzy systems and control: design and stability analysis, (1994)
[24] Ying, H.: Fuzzy control and modeling: analytical foundations and applications, (2000)
[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, No. 5, 625-629 (1999)
[28] Zadeh, L. A.: Is there a need for fuzzy logic?, Information sciences 178, No. 13, 2751-2779 (2008) · Zbl 1148.68047 · doi:10.1016/j.ins.2008.02.012
[29] Zarandi, M. H. Fazel; Alaeddini, A.: A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts, Information sciences 180, No. 16, 3033-3044 (2010)
[30] Zhang, Z.; Cai, K. -Y.: Optimal fuzzy reasoning and its robustness analysis, International journal of intelligent systems 19, No. 11, 1033-1049 (2004) · Zbl 1101.68889 · doi:10.1002/int.20035
[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, No. 6, 540-558 (2010) · Zbl 1192.68691 · doi:10.1002/int.20420