Research article

Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

  • Received: 22 June 2020 Accepted: 20 July 2020 Published: 29 July 2020
  • MSC : 68XX, 68Uxx

  • Type-reduction (TR) is a key block for interval type-2 fuzzy logic systems (IT2 FLSs). In general, Karnik-Mendel (KM) (or enhanced Karnik-Mendel (EKM)) algorithms are used to perform the TR. These two types of algorithms have the advantage of preserving the uncertainties of membership functions (MFs) flow in IT2 FLSs. This paper gives the initialization explanations of KM and EKM algorithms, and proposes reasonable initialization enhanced Karnik-Mendel (RIEKM) algorithms for centroid TR of IT2 FLSs. By considering the accurate continuous Nie-Tan (CNT) algorithms as the benchmark, four computer simulation examples are adopted to illustrate and analyze the performances of RIEKM algorithms for solving the centroid TR and defuzzification of IT2 FLSs. Compared with the EKM algorithms, the proposed RIEKM algorithms have smaller absolute errors and faster convergence speeds, which afford the potential value for designing and applying IT2 FLSs.

    Citation: Yang Chen, Jinxia Wu, Jie Lan. Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems[J]. AIMS Mathematics, 2020, 5(6): 6149-6168. doi: 10.3934/math.2020395

    Related Papers:

  • Type-reduction (TR) is a key block for interval type-2 fuzzy logic systems (IT2 FLSs). In general, Karnik-Mendel (KM) (or enhanced Karnik-Mendel (EKM)) algorithms are used to perform the TR. These two types of algorithms have the advantage of preserving the uncertainties of membership functions (MFs) flow in IT2 FLSs. This paper gives the initialization explanations of KM and EKM algorithms, and proposes reasonable initialization enhanced Karnik-Mendel (RIEKM) algorithms for centroid TR of IT2 FLSs. By considering the accurate continuous Nie-Tan (CNT) algorithms as the benchmark, four computer simulation examples are adopted to illustrate and analyze the performances of RIEKM algorithms for solving the centroid TR and defuzzification of IT2 FLSs. Compared with the EKM algorithms, the proposed RIEKM algorithms have smaller absolute errors and faster convergence speeds, which afford the potential value for designing and applying IT2 FLSs.


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    [1] D. R. Wu, J. M. Mendel, Uncertainty measures for interval type-2 fuzzy sets, Inf. Sci., 177 (2007), 5378-5393. doi: 10.1016/j.ins.2007.07.012
    [2] J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Englewood Cliffs, NJ, USA: Prentice-Hall, 2001, 1-547.
    [3] P. Melin, L. Astudillo, O. Castillo, et al. Optimal design of type-2 and type-1 fuzzy tracking controllers for autonomous mobile robots under perturbed torques using a new chemical optimization paradigm, Expert Syst. Appl., 40 (2013), 3185-3195. doi: 10.1016/j.eswa.2012.12.032
    [4] H. Hagras, A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots, IEEE Trans. Fuzzy Syst., 12 (2004), 524-539. doi: 10.1109/TFUZZ.2004.832538
    [5] C. W. Tao, J. S. Taur, C. W. Chang, et al. Simplified type-2 fuzzy sliding controller for wing rocket system, Fuzzy Sets Syst., 207 (2012), 111-129. doi: 10.1016/j.fss.2012.02.015
    [6] D. Bernardo, H. Hagras, E. Tsang, A genetic type-2 fuzzy logic based system for the generation of summarized linguistic predictive models for financial applications, Soft Comput., 17 (2013), 2185-2201.
    [7] Y. Chen, D. Z. Wang, S. C. Tong, Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: With combination of BP algorithms and KM algorithms, Neurocomputing, 174 (2016), 1133-1146.
    [8] A. Khosravi, S. Nahavandi, D. Creighton, et al., Interval type-2 fuzzy logic systems for load forecasting: a comparative study, IEEE Trans. Power Syst., 27 (2012), 1274-1282. doi: 10.1109/TPWRS.2011.2181981
    [9] S. Barkat, A. Tlemcani, H. Nouri, Noninteracting adaptive control of PMSM using interval type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst., 19 (2011), 925-936. doi: 10.1109/TFUZZ.2011.2152815
    [10] D. Z. Wang, Y. Chen, Study on permanent magnetic drive forecasting by designing Takagi Sugeno Kang type interval type-2 fuzzy logic systems, Trans. Institute Meas. Control, 40 (2018), 2011-2023.
    [11] Y. Chen, D. Z. Wang, Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms, Trans. Institute Meas. Control, 41 (2019), 2886-2896.
    [12] P. Melin, O. Mendoza, O. Castillo, An improved method for edge detection based on interval type-2 fuzzy logic, Expert Syst. Appl., 37 (2010), 8527-8535.
    [13] C. S. Lee, M. H. Wang, H. Hagras, Type-2 fuzzy ontology and its application to personal diabetic-diet recommendation, IEEE Trans. Fuzzy Syst., 18 (2010), 316-328.
    [14] G. M. Méndez, M. D. L. A. Hernandez, Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods, Inf. Sci., 179 (2009), 2146-2157.
    [15] G. M. Méndez, M. D. L. A. Hernandez, Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems, Inf. Sci., 220 (2013), 149-169. doi: 10.1016/j.ins.2012.01.024
    [16] T. Wang, Y. Chen, S. C. Tong, Fuzzy reasoning models and algorithms on type-2 fuzzy sets, Int. J. Innovative Comput. Inf. Control, 4 (2008), 2451-2460.
    [17] J. M. Mendel, General type-2 fuzzy logic systems made simple: A tutorial, IEEE Trans. Fuzzy Sys., 22 (2014), 1162-1182.
    [18] J. M. Mendel, On KM algorithms for solving type-2 fuzzy set problems, IEEE Trans. Fuzzy Syst., 21 (2013), 426-446. doi: 10.1109/TFUZZ.2012.2227488
    [19] D. R. Wu, J. M. Mendel, Enhanced Karnik-Mendel algorithms, IEEE Trans. Fuzzy Syst., 17 (2009), 923-934. doi: 10.1109/TFUZZ.2008.924329
    [20] J. M. Mendel, F. L. Liu, Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set, IEEE Trans. Fuzzy Syst., 15 (2007), 309-320. doi: 10.1109/TFUZZ.2006.882463
    [21] X. W. Liu, J. M. Mendel, D. R. Wu, Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements, Inf. Sci., 184 (2012), 75-91. doi: 10.1016/j.ins.2011.07.042
    [22] J. W. Li, R. John, S. Coupland, et al., On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets, IEEE Trans. Fuzzy Syst., 26 (2018), 1036-1039.
    [23] Y. Chen, Study on weighted Nagar-Bardini algorithms for centroid type-reduction of interval type-2 fuzzy logic systems, J. Intell. Fuzzy Syst., 34 (2018), 2417-2428.
    [24] J. M. Mendel, R. I. John, F. L. Liu, Interval type-2 fuzzy logic systems made simple, IEEE Trans. Fuzzy Syst., 14 (2006), 808-821. doi: 10.1109/TFUZZ.2006.879986
    [25] Y. Chen, D. Z. Wang, Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted Nie-Tan algorithms, Soft Comput., 22 (2018), 7659-7678.
    [26] F. L. Liu, An efficient centroid type-reduction strategy for general type-2 fuzzy logic system, Inf. Sci., 178 (2008), 2224-2236. doi: 10.1016/j.ins.2007.11.014
    [27] J. M. Mendel, X. W. Liu, Simplified interval type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst., 21 (2013), 1056-1069.
    [28] S. Greenfield, F. Chiclana, Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set, Int. J. Approximate Reasoning, 54 (2013), 1013-1033.
    [29] Y. Chen, Study on centroid type-reduction of interval type-2 fuzzy logic systems based on noniterative algorithms, Complexity, 2019 (2019), 1-12.
    [30] T. Kumbasar, Revisiting Karnik-Mendel algorithms in the framework of linear fractional programming, Int. J. Approximate Reasoning, 82 (2017), 1-21.
    [31] S. Greenfield, F. Chiclana, S. Coupland, et al., The collapsing method of defuzzification for discretised interval type-2 fuzzy sets, Inf. Sci., 179 (2009), 2055-2069. doi: 10.1016/j.ins.2008.07.011
    [32] D. R. Wu, Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons, IEEE Trans. Fuzzy Syst., 21 (2013), 80-99.
    [33] M. A. Khanesar, A. Jalalian, O. Kaynak, Improving the speed of center of set type-reduction in interval type-2 fuzzy systems by eliminating the need for sorting, IEEE Trans. Fuzzy Syst., 25 (2017), 1193-1206. doi: 10.1109/TFUZZ.2016.2602392
    [34] Y. Chen, D. Z. Wang, W. Ning, Forecasting by TSK general type-2 fuzzy logic systems optimized with genetic algorithms, Optimal Control Appl. Methods, 39 (2018), 393-409.
    [35] Y. Chen, D. Z. Wang, Forecasting by general type-2 fuzzy logic systems optimized with QPSO algorithms, Int. J. Control, Automation Syst., 15 (2017), 2950-2958.
    [36] F. Gaxiola, P. Melin, F. Valdez, et al. Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Appl. Soft Comput., 38 (2016), 860-871. doi: 10.1016/j.asoc.2015.10.027
    [37] Q. F. Fan, T. Wang, Y. Chen, et al., Design and application of interval type-2 TSK fuzzy logic system based on QPSO algorithm, Int. J. Fuzzy Syst., 20 (2018), 835-846. doi: 10.1007/s40815-017-0357-3
    [38] C. H. Hsu, C. F. Juang, Evolutionary robot wall-following control using type- 2 fuzzy controller with species-de-activated continuous ACO, IEEE Trans. Fuzzy Syst., 21 (2013), 100-112.
    [39] D. R. Wu, J. M. Mendel, Recommendations on designing practical interval type-2 fuzzy systems, Eng. Appl. Artif. Intell., 85 (2019), 182-193.
    [40] X. L. Liu, S. P. Wan, Combinatorial iterative algorithms for computing the centroid of an interval type-2 fuzzy set, IEEE Trans. Fuzzy Syst., 2019, DOI: 10.1109/TFUZZ.2019.2911918.
    [41] H. Z. Hu, Y. Wang, Y. L. Cai, Advantages of the enhanced opposite direction searching algorithm for computing the centroid of an interval type-2 fuzzy set, Asian J. Control, 14 (2012), 1422-1430.
    [42] J. H. Hu, P. P. Chen, Y. Yang, The fruit fly optimization algorithms for patient-centered care based on interval trapezoidal type-2 fuzzy numbers, Int. J. Fuzzy Syst., 21 (2019), 1270-1287.
    [43] M. Javanmard, H. Mishmast Nehi, A solving method for fuzzy linear programming problem with interval type-2 fuzzy numbers, Int. J. Fuzzy Syst., 21 (2019), 882-891.
    [44] C. Chen, R. John, J. Twycross, et al. A direct approach for determining the switch points in the Karnik-Mendel algorithm, IEEE Trans. Fuzzy Syst., 26 (2018), 1079-1085. doi: 10.1109/TFUZZ.2017.2699168
    [45] O. Castillo, L. Amador-Angulo, J. R. Castro, et al. A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems, Inf. Sci., 354 (2016), 257-274.
    [46] L. Cervantes, O. Castillo, Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control, Inf. Sci., 324 (2015), 247-256.
    [47] O. Castillo, P. Melin, E. Ontiveros, et al. A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics, Eng. Appl. Artificial Intelligence, 85 (2019), 666-680.
    [48] E. Ontiveros-Robles, P. Melin, O. Castillo, Comparative analysis of noise robustness of type 2 fuzzy logic controllers, Kybernetika, 54 (2018), 175-201.
    [49] E. Ontiveros-Robles, P. Melin, O. Castillo, New methodology to approximate type-reduction based on a continuous root-finding karnik mendel algorithm, Algorithms, 10 (2017), 77-96. doi: 10.3390/a10030077
    [50] Y. Chen, Study on sampling-based discrete noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems, Soft Comput., 24 (2020), 11819-11828.
    [51] S. C. Tong, Y. M. Li, Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties, Sci. China Inf. Sci., 53 (2010), 307-324. doi: 10.1007/s11432-010-0031-y
    [52] S. C. Tong, Y. M. Li, Observer-based adaptive fuzzy backstepping control of uncertain pure-feedback systems, Sci. China Inf. Sci., 57 (2014), 1-14.
    [53] M. Deveci, I. Z. Akyurt, S. Yavuz, GIS-based interval type-2 fuzzy set for public bread factory site selection, J. Enterprise Inf. Manage., 31 (2018), 820-847.
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