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Volume 54 Issue 2
Jun.  2019
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Article Contents
Journal of Southwest Jiaotong University  > 2019  >  54(2): 436-444.
ZHAO Taoyan, LI Ping, CAO Jiangtao. Overview of Type-Reduction Algorithms for Type-2 Fuzzy Logic Systems[J]. Journal of Southwest Jiaotong University, 2019, 54(2): 436-444. doi: 10.3969/j.issn.0258-2724.20170060
Citation: ZHAO Taoyan, LI Ping, CAO Jiangtao. Overview of Type-Reduction Algorithms for Type-2 Fuzzy Logic Systems[J]. Journal of Southwest Jiaotong University, 2019, 54(2): 436-444. doi: 10.3969/j.issn.0258-2724.20170060
shu

Overview of Type-Reduction Algorithms for Type-2 Fuzzy Logic Systems

doi: 10.3969/j.issn.0258-2724.20170060
  • Received Date: 19 Jan 2017
  • Rev Recd Date: 04 Apr 2018
    • Available Online: 23 Apr 2018
  • Publish Date: 01 Apr 2019
    Abstract
  • The computation precision, computation time, and the loss of system information of the type-reduction process have a great influence on the performance of type-2 fuzzy logic systems. In this paper, the basic concept of type-2 fuzzy sets and the computation process of type-2 fuzzy logic systems are briefly introduced. Then, a detailed review of the research on type-reduction algorithms is given for both interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems. The computational complexity of different type-reduction algorithms is analyzed and compared. Finally, the problems faced with each type-reduction algorithm are summarized, and potential future research directions are presented. The computation cost of type-reduction algorithms remains as the bottleneck in type-2 fuzzy logic system improvement. The key direction of future research should be the improvement of the theory behind type-reduction algorithms, the solving of the computational complexity through mathematical methods, and applying this to real-time systems.

     

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  • ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(13): 338-353.
    COUPLAND S, JOHN R I. Type-2 fuzzy logic and the modeling of uncertainty[M]. Berlin: Springer-Verlag, 2008: 3-22
    ZADEH L A. The concept of a linguistic variable and its application to approximate reasoning-I[J]. Information Sciences, 1975, 8(1): 199-249.
    HISDAL E. The IF THEN ELSE statement and interval-valued fuzzy sets of higher type[J]. International Journal of Man-Machine Studies, 1981, 15(44): 385-455.
    JANA D K, BEJ B, WAHAB M H A, et al. Novel type-2 fuzzy logic approach for inference of corrosion failure likelihood of oil and gas pipeline industry[J]. Engineering Failure Analysis, 2017, 80: 299-311. doi: 10.1016/j.engfailanal.2017.06.046
    TAYYEBI S, SOLTANALI, S. A new approach of GA-based type reduction of interval type-2 fuzzy model for nonlinear MIMO system:application in methane oxidtion process[J]. Chemonmetrics and Intelligent Laboratory Systems, 2017, 167: 152-160. doi: 10.1016/j.chemolab.2017.06.004
    COTELI R, ACIKGOZ H, UCAR F, et al. Design and implementation of type-2 neural system controller for PWM rectifiers[J]. International Journal of Hydrogen Energy, 2017, 42(32): 20759-20771. doi: 10.1016/j.ijhydene.2017.07.032
    CASTILLO O, CERVANTES L, SORIA J, et al. A generalized type-2 fuzzy granular approach with application to aerospace[J]. Information Sciences, 2016, 354: 165-177. doi: 10.1016/j.ins.2016.03.001
    MENDEL J M. Type-2 fuzzy sets and systems[J]. IEEE Computational Intelligence Magazine, 2007, 2(1): 20-29. doi: 10.1109/MCI.2007.380672
    WU H, MENDEL J M. Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems[J]. IEEE Transactions on Fuzzy Systems, 2002, 10(5): 622-639. doi: 10.1109/TFUZZ.2002.803496
    胡怀中,张伟斌,杨华南. 区间型二型模糊集重心的直接Karnik-Mendel算法[J]. 系统仿真学报,2010,22(10): 2326-2328.

    HU Huaizhong, ZHANG Weibin, YANG Huanan. Dieect Karnik-Mendel algorithm in interval type-2 fuzzy system[J]. Journal of System Simulation, 2010, 22(10): 2326-2328.
    MAITY S, SIL J. Tuning of centroid with modified Keinik-Mendel (KM) algorithm[J]. International Journal of Modeling and Optimization, 2012, 2(6): 718-722.
    MENDEL J M, LIU X. New closed-form solution for Karnik-Mendel algorithm dezuzzification of an interval type-2 set[C]//IEEE International Conference on Fuzzy Systems. [S.l.]: IEEE, 2012: 1-8
    LIU X, QIN Y, WU L. Fast and direct Karnik-Mendel algorithm computation for the centroid of an interval type-2 fuzzy set[C]//IEEE International Conference on Fuzzy Systems. Brisbane: IEEE, 2012: 1058-1065
    KUMBASAR T. Revisiting KM algorithms: a linear progarmming approach[C]//IEEE International Conference on Fuzzy Systems. Istanbul: IEEE, 2015: 1-6
    DODURKA M F, KUMBASAR T, SAKALLI A, et al. Boundary function based Karnik-Mendel type reduction method for interval type-2 fuzzy PID controllers[C]//IEEE International Conference on Fuzzy Systems. Beijing: IEEE, 2014: 619-625
    SALAKEN S M, KHOSRAVI A, WU D R. Switch point finding using polynomial regression for fuzzy type reduction algorithms[C]//IEEE International Conference on Fuzzy Systems. Istanbul: IEEE, 2015: 45-50
    LIU X W. Extension of Karnik-Mendel algorithms with uncertainty bound method[C]//International Conference on System Science and Engineering. Dalian: IEEE, 2012: 459-464
    KHANESAR M A, KAYNAK O and GAO H J. Improved Karnik-Mendel algorithm: eliminating the need for sorting[C]//International Conference on Mechatronics and Control. Jinzhou: [s.n.], 2014: 204-209
    陈阳,王大志. 基于加权Karnik-Mendel算法的区间二型模糊逻辑系统降型[J]. 控制理论与应用,2016,33(10): 1327-1336.

    CHEN Yang, WANG Dazhi. Type-reduction of interval type-2 fuzzy logic systems with weighted Karnik-Mendel algorithms[J]. Control Theory and Applications, 2016, 33(10): 1327-1336.
    WU D, MENDEL J M. Enhanced Karnik-Mendel algorithms[J]. IEEE Transactions on Fuzzy Systems, 2009, 17(4): 923-934. doi: 10.1109/TFUZZ.2008.924329
    王建辉,纪雯,方晓柯,等. 对区间二型模糊集的EKM降型法的改进[J]. 控制与决策,2013,28(8): 1165-1172.

    WANG Jianhui, JI Wen, FANG Xiaoke, et al. Improvement of enhanced Karnik-Mendel algorithm for interval type-2 fuzzy sets[J]. Control and Decision, 2013, 28(8): 1165-1172.
    SALAKEN S M, KHOSRAVI A, WU D R. Effect of different initializations on EKM algorithm[C]//IEEE International Conference on Fuzzy Systems. Istanbul: IEEE, 2015: 1-6
    YEH C, JENG W, LEE S. An enhanced type-reduction algorithm for type-2 fuzzy sets[J]. IEEE Transactions on Fuzzy Systems, 2011, 19(2): 227-240. doi: 10.1109/TFUZZ.2010.2093148
    MELGAREJO M. A fast recursive method to compute the generalized centroid of an interval type-2 fuzzy set[C]//Proc. of Annual Conference of the North American Fuzzy Information Processing Society. San Diego: [s.n.], 2007: 190-194
    DURAN K, BERNAL H, MELGAREJO M. Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set[C]//Annual Meeting of the North American Fuzzy Information Processing Society. New York: [s.n.], 2008: 1-5
    WU D. Approaches for reducing the computational cost of interval type-2 fuzzy logic systems:overview and comparisons[J]. IEEE Transactions on Fuzzy Systems, 2013, 21(1): 80-99. doi: 10.1109/TFUZZ.2012.2201728
    CHEN Y, WANG D. Studies on centroid type-reduction algorithms for interval type-2 fuzzy logic systems[C]//IEEE Fifth International Conference on Big Data and Cloud Computing. Dalian: IEEE, 2015: 344-349
    施建中,李荣,杨勇. 一种新的区间二型模糊集合降阶算法[J]. 计算机应用研究,2017,34(2): 378-381. doi: 10.3969/j.issn.1001-3695.2017.02.013

    SHI Jianzhong, LI Rong, YANG Yong. New interval type-2 fuzzy sets type reduction algorithm[J]. Application Research of Computers, 2017, 34(2): 378-381. doi: 10.3969/j.issn.1001-3695.2017.02.013
    WU D R, NIE M. Comparison and practical implementation of type-reduction algorithms for type-2 fuzzy sets and systems[C]//IEEE International Conference on Fuzzy Systems. Taipei: IEEE, 2011: 2131-2138
    HU H, WANG Y, CAI Y. Advantages of the enhanced opposite direction searching algorithm for computing the centroid of an interval type-2 fuzzy set[J]. Asian Journal of Control, 2012, 14(6): 1-9.
    LIU X W, ZHU Q, GUO S. Three new uncertainty bound methods of Karnik-Mendel algorithms[C]//IEEE International Conference on Fuzzy Systems, Monterey. [S.l.]: IEEE, 2013: 1-8
    ZARANDI M H F, TORSHIZI A D, TURKSEN I B, et al. A new indirect approach to the type-2 fuzzy systems modeling and design[J]. Information Sciences, 2013, 232(5): 346-365.
    JUANG C F, JUANG K J. Reduced interval type-2 neural fuzzy system using weighted bound-set boundary operation for computation speedup and chip implementation[J]. IEEE Transactions on Fuzzy Systems, 2013, 21(3): 477-491. doi: 10.1109/TFUZZ.2012.2230179
    NIE M, TAN W W. Towards an efficient type-reduction method for interval type-2 fuzzy logic systems[C]//IEEE International Conference on Fuzzy Systems. Hong Kong: IEEE, 2008: 1425-1432
    BEGIAN M, MELEK W, MENDEL J. Stability analysis of type-2 fuzzy systems[C]//IEEE International Conference on Fuzzy Systems. Hong Kong: IEEE, 2008: 947-953
    PEDRO P C, ARTURO M, ARTURO T V. Hardware type-2 fuzzy logic position controller based on Karnik-Mendel algorithms[J]. Journal of Control Science and Engineering, 2013, 7(1): 1-12.
    KHANESAR M A, MENDEL J M. Maclaurin series expansion complexity-reduced center of sets type-reduction+defuzzification for interval type-2 fuzzy systems[C]//IEEE International Conference on Fuzzy Systems. Vancouver: IEEE, 2016: 1224-1231
    KHOSRAVI A, NAHAVANDI S, KHOSRAVI R. Evaluation and comparison of type reduction algorithms from a forecast accuracy perspective[C]//IEEE International Conference on Fuzzy Systems. Hyderabad: IEEE, 2013: 1-7
    GORZALCZANY M. Decision making in signal transmission problems with interval-valued fuzzy sets[J]. Fuzzy Sets and Systems, 1987, 23(2): 191-203. doi: 10.1016/0165-0114(87)90058-3
    LIANG Q, MENDEL J M. Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters[J]. IEEE Transactions on Systems, 2000, 8(5): 551-563.
    WU D, TAN W W. Computationally efficient type-reduction strategies for a type-2 fuzzy logic controller[C]//IEEE International Conference on Fuzzy Systems. Reno: IEEE, 2005: 353-358
    LI C, YI J, ZHAO D. A novel type-reduction method for interval type-2 fuzzy logic systems[C]//International Conference on Fuzzy Systems and Knowledge Discovery. Jinan: [s.n.], 2008: 157-161
    DU X, YING H. Derivation and analysis of the analytical structures of the interval type-2 fuzzy PI and PD controllers[J]. IEEE Transactions on Fuzzy Systems, 2010, 18(4): 802-814. doi: 10.1109/TFUZZ.2010.2049022
    TAO C W, TAUR J S, CHANG C W, et al. Simplified type-2 fuzzy sliding controller for wing rock system[J]. Fuzzy Sets and Systems, 2012, 207(8): 111-129.
    GREENFIELD S, CHICLANA F, COUPLAND S, et al. The collapsing method of defuzzification for discretised interval type-2 fuzzy sets[J]. Information Sciences, 2009, 179(13): 2055-2069. doi: 10.1016/j.ins.2008.07.011
    WU D R. An overview of alternative type-reduction approaches for reducing the computational cost of interval type-2 fuzzy logic controllers[C]//IEEE World Congress on Computational Intelligence. Brisbane: IEEE, 2012: 1-8
    TORSHIZI A D, ZARANDI M H F, ZAKERI H. On type-reduction of type-2 fuzzy sets: a review[J]. Applied Soft Computing, 2015, 27: 614-627.
    LU T C. Genetic-algorithm-based type reduction algorithm for interval type-2 fuzzy logic controllers[J]. Engineering Applications of Artificial Intelligence, 2015, 42: 36-44. doi: 10.1016/j.engappai.2015.02.012
    ZHAO X Z, GAO Y B, ZENG J F, et al. PSO type-reduction method for geometric interval type-2 fuzzy logic systems[J]. Journal of Harbin Institute of Technology (New Series), 2008, 15(6): 862-867.
    ULU C, GUZELKAYA M, EKSIN I. A dynamic defuzzication method for interval type-2 fuzzy logic controllers[C]//IEEE International Conference on Mechatronics. Istanbul: IEEE, 2011: 318-323
    LU T C, CHEN S L. A new type reduction method for type-2 fuzzy logic controller[C]//International Automatic Control Conference. Nantou: [s.n.], 2013: 334-338
    TAO C W, CHANG C W, TAUR J S. A simplify type reduction for interval type-2 fuzzy sliding controller[J]. International Journal of Fuzzy Systems, 2013, 15(4): 460-470.
    CHEN C L, CHEN S C, KUO Y H. The reduction of interval type-2 LR fuzzy sets[J]. IEEE Transactions on Fuzzy Systems, 2014, 22(4): 840-858. doi: 10.1109/TFUZZ.2013.2277729
    KHOSRAVI A, NAHAVANDI S. Load forecasting using interval type-2 fuzzy logic systems:optimal type reduction[J]. IEEE Transactions on Industrial Informatics, 2014, 10(2): 1055-1063. doi: 10.1109/TII.2013.2285650
    COUPLAND S, JOHN R I. An investigation into alternative methods for the defuzzification of an interval type-2 fuzzy set[C]//IEEE International Conference on Fuzzy Systems. Vancouver: IEEE, 2006: 1425-1432
    CHAO C C, HSIAO M Y, TSAI S H, et al. Design of an interval type-2 fuzzy immune controller[J]. Information Technology Journal, 2010, 9(6): 1115-1123. doi: 10.3923/itj.2010.1115.1123
    JOHN R I, COUPLAND S. Type-2 fuzzy logic:a historical view[J]. IEEE Computational Intelligence Magazine, 2007, 2(1): 57-62. doi: 10.1109/MCI.2007.357194
    GONZALEZ C, CASTRO J R, MELIN P, et al. An edge detection method based on generalized type-2 fuzzy logic[J]. Soft Computing, 2016, 20(2): 773-784. doi: 10.1007/s00500-014-1541-0
    GREENFIELD S. Type-2 fuzzy logic: circumventing the defuzzification bottleneck[D]. Leicester: De Montfort University, 2012
    LIU F. An efficient centroid type-reduction strategy for general type-2 fuzzy logic system[J]. Information Science, 2008, 178(9): 2224-2236.
    XIE B K, LEE S J. An extended type-reduction method for general type-2 fuzzy sets[J]. IEEE Transactions on Fuzzy Systems, 2015, 14(8): 1-10.
    WU H J, SU Y L, LEE S J. A fast method for computing the centroid of a type-2 fuzzy set[J]. IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics, 2012, 42(3): 764-777. doi: 10.1109/TSMCB.2011.2177085
    WAGNER C, HAGRAS H. zSlices based general type-2 FLC for the control of autonomous mobile robots in real word environment[C]//IEEE International Conference on Fuzzy Systems. Jeju Island: IEEE, 2009: 718-725
    ZHAI D, MENDEL J. Comment toward general type-2 fuzzy logic systems based on zSlices[J]. IEEE Transactions on Fuzzy Systems, 2012, 20(5): 996-997. doi: 10.1109/TFUZZ.2012.2190076
    WAGNER C, HAGRAS H. Towards general type-2 fuzzy logic systems based on zSlices[J]. IEEE Transactions on Fuzzy Systems, 2010, 18(4): 637-660. doi: 10.1109/TFUZZ.2010.2045386
    ROBERT I. Perception modelling using type-2 fuzzy sets[D]. Leicester: De Montfort University, 2000
    LUCAS L, CENTENO T, DELGADO M. General type-2 fuzzy inference systems: analysis, design and computational aspects[C]//IEEE International Conference on Fuzzy Systems. London: IEEE, 2007: 1-6
    GREENFIELD S, CHICLANA F. Defuzzification of the discretised generalised type-2 fuzzy set:experimental evaluation[J]. Information Sciences, 2013, 244(7): 1-25.
    GREENELD S, JOHN R I. Fuzzy logic and computational geometry[C]//Proceedings of the International Conference on Recent Advances in Soft Computing. Leicester: IEEE, 2004: 3-8
    COUPLAND S, JOHN R I. Geometric type-2 sets[M]. New York: Springer, 2013: 81-96
    COUPLAND S, JOHN R I. New geometric inference techniques for type-2 fuzzy sets[J]. International Journal of Approximate Reasoning, 2008, 49(1): 198-211. doi: 10.1016/j.ijar.2008.03.001
    GREENFIELD S, CHICLANA F, JOHN R I. Type-reduction of the discretised interval type-2 fuzzy set[C]//IEEE International Conference on Fuzzy Systems. Jeju Island: IEEE, 2009: 738-743
    GREENFIELD S, JOHN R I, COUPLAND S. A novel sampling method for type-2 defuzzification[C]//Proceedings of UKCI 2005. London: IEEE, 2005: 120-127
    ZHAI D, MENDEL J. Centroid of a general type-2 fuzzy set computed by means of the centroid-flow algorithm[C]//IEEE International Conference on Fuzzy Systems. Barcelona: IEEE, 2010: 895-902
    GAFA C, COUPLAND S. A new recursive type-reduction procedure for general type-2 fuzzy sets[C]//IEEE Symposium on Advances in Type-2 Fuzzy Logic Systems. Paris: IEEE, 2011: 44-49
    CHICLANA F, ZHOU S M. Type-reduction of general type-2 fuzzy sets:the tyep-1 OWA Approach[J]. International Journal of Intelligent Systems, 2013, 28(5): 505-522. doi: 10.1002/int.2013.28.issue-5
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