Research article

Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

  • Received: 03 August 2020 Accepted: 07 October 2020 Published: 14 October 2020
  • MSC : 68XX, 68Uxx

  • Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of weighted-based noniterative according to the Newton-Cotes quadrature formulas in numerical integration techniques. Moreover, the continuous noniterative algorithms are considered as the benchmarks for computing. Four simulation experiments are provided to illustrate the performances of weighted-based noniterative algorithms for computing the defuzzified values of IT2 FLSs. Compared with the original noniterative algorithms, the proposed weighted-based algorithms can obtain smaller absolute errors and faster convergence speeds under the same sampling rate, which afford the potential values for designing T2 FLSs.

    Citation: Yang Chen, Jinxia Wu, Jie Lan. Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems[J]. AIMS Mathematics, 2020, 5(6): 7719-7745. doi: 10.3934/math.2020494

    Related Papers:

  • Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of weighted-based noniterative according to the Newton-Cotes quadrature formulas in numerical integration techniques. Moreover, the continuous noniterative algorithms are considered as the benchmarks for computing. Four simulation experiments are provided to illustrate the performances of weighted-based noniterative algorithms for computing the defuzzified values of IT2 FLSs. Compared with the original noniterative algorithms, the proposed weighted-based algorithms can obtain smaller absolute errors and faster convergence speeds under the same sampling rate, which afford the potential values for designing T2 FLSs.


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    [1] O. Castillo, P. Melin, Type-2 fuzzy logic theory and applications, Berlin, Germany: Springer-Verlag, 2008.
    [2] H. Hagras, C. Wagner, Towards the wide spread use of type-2 fuzzy logic systems in real world applications, IEEE Comput. Intell. M., 7 (2012), 14-24.
    [3] 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.
    [4] D. Z. Wang, Y. Chen, Study on permanent magnetic drive forecasting by designing Takagi Sugeno Kang type interval type-2 fuzzy logic systems, T. I. Meas. Control, 40 (2018), 2011-2023.
    [5] S. Barkat, A. Tlemcani, H. Nouri, Noninteracting adaptive control of PMSM using interval type-2 fuzzy logic systems, IEEE T. Fuzzy Syst., 19 (2011), 925-936.
    [6] Y. Chen, D. Z. Wang, Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms, T. I. Meas. Control, 41 (2019), 2886-2896.
    [7] B. Safarinejadian, P. Ghane, H. Monirvaghefi, Fault detection in non-linear systems based on type-2 fuzzy logic, International Journal of Systems Sciences, 46 (2015), 394-404.
    [8] C. S. Lee, M. H. Wang, H. Hagras, Type-2 fuzzy ontology and its application to personal diabetic-diet recommendation, IEEE T. Fuzzy Syst., 18 (2010), 316-328.
    [9] O. Mendoza, P. Melin, O. Castillo, Interval type-2 fuzzy logic and modular networks for face recognition applications, Appl. Soft Comput., 9 (2009), 1377-1387.
    [10] A. Niewiadomski, On finity, countability, cardinalities, and cylindric extensions of type-2 fuzzy sets in linguistic summarization of databases, IEEE T. Fuzzy Syst., 18 (2010), 532-545.
    [11] J. M. Mendel, R. I. John, F. L. Liu, Interval type-2 fuzzy logic systems made simple, IEEE T. Fuzzy Syst., 14 (2006), 808-821.
    [12] J. M. Mendel, General type-2 fuzzy logic systems made simple: a tutorial, IEEE T. Fuzzy Syst., 22 (2014), 1162-1182.
    [13] J. M. Mendel, On KM algorithms for solving type-2 fuzzy set problems, IEEE T. Fuzzy Syst., 21 (2013), 426-446.
    [14] 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 T. Fuzzy Syst., 15 (2007), 309-320.
    [15] D. R. Wu, J. M. Mendel, Enhanced Karnik-Mendel algorithms, IEEE T. Fuzzy Syst., 17 (2009), 923-934.
    [16] X. W. Liu, J. M. Mendel, D. R. Wu, Study on enhanced Karnik-Mendel algorithms: initialization explanations and computation improvements, Inform. Sciences, 184 (2012), 75-91.
    [17] Y. Chen, D. Z. Wang, Study on centroid type-reduction of general type-2 fuzzy logic systems with weighted enhanced Karnik-Mendel algorithms, Soft Comput., 22 (2018), 1361-1380.
    [18] Y. Chen, Study on centroid type-reduction of interval type-2 fuzzy logic systems based on noniterative algorithms, Complexity, 2019 (2019), 1-12.
    [19] A. M. EI-Nagar, M. EI-Bardini, Simplified interval type-2 fuzzy logic system based on new type-reduction, J. Intell. Fuzzy Syst., 27 (2014), 1999-2010.
    [20] J. W. Li, R. John, S. Coupland, G. Kendall, On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets, IEEE T. Fuzzy Syst., 26 (2018), 1036-1039.
    [21] M. Biglarbegian, W. W. Melek, J. M. Mendel, On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling, Inform. Sciences, 181 (2011), 1325-1347.
    [22] M. Biglarbegian, W. W. Melek, J. M. Mendel, On the stability of interval type-2 TSK fuzzy logic systems, IEEE T. Cybernetics, 40 (2010), 798-818.
    [23] S. Greenfield, F. Chiclana, S. Coupland, R. John, The collapsing method of defuzzification for discretised interval type-2 fuzzy sets, Inform. Sciences, 179 (2009), 2055-2069.
    [24] H. W. Wu, J. M. Mendel, Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems, IEEE T. Fuzzy Syst., 10 (2002), 622-639.
    [25] M. d. l. A. Hernandez, P. Melin, G. M. Méndez, O. Castillo, I. López-Juarez, A hybrid learning method composed by the orthogonal least-squares and the back-propagation learning algorithms for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic systems, Soft Comput., 19 (2015), 661-678.
    [26] Y. Chen, D. Z. Wang, W. Ning, Forecasting by TSK general type-2 fuzzy logic systems optimized with genetic algorithms, Optim. Contr. Appl. Met., 39 (2018), 393-409.
    [27] A. Khosravi, S. Nahavandi, Load forecasting using interval type-2 fuzzy logic systems: optimal type reduction, IEEE T. Ind. Inform., 10 (2014), 1055-1063.
    [28] C. Wagner, H. Hagras, Towards general type-2 fuzzy logic systems based on zSlices, IEEE T. Fuzzy Syst., 18 (2010), 637-660.
    [29] S. Greenfield, F. Chiclana, Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set, Int. J. Approx. Reason., 54 (2013), 1013-1033.
    [30] J. H. Mathews, K. K. Fink, Numerical Methods Using Matlab, Prentice-Hall Inc, Upper Saddle River, NJ, 2004.
    [31] X. W. Liu, J. M. Mendel, Connect Karnik-Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set, IEEE T. Fuzzy Syst., 19 (2011), 652-665.
    [32] Y. Chen, Study on sampling based discrete Nie-Tan algorithms for computing the centroids of general type-2 fuzzy sets, IEEE Access, 7 (2019), 156984-156992.
    [33] D. R. Wu, Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons, IEEE T. Fuzzy Syst., 21 (2013), 80-99.
    [34] 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 T. Fuzzy Syst., 25 (2017), 1193-1206.
    [35] D. R. Wu, J. M. Mendel, Recommendations on designing practical interval type-2 fuzzy systems, Eng. Appl. Artif. Intel., 85 (2019), 182-193.
    [36] F. Gaxiola, P. Melin, F. Valdez, J. R. Castro, O. Castillo, Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Appl. Soft Comput., 38 (2016), 860-871.
    [37] C. H. Hsu, C. F. Juang, Evolutionary robot wall-following control using type- 2 fuzzy controller with species-de-activated continuous ACO, IEEE T. Fuzzy Syst., 21 (2013), 100-112.
    [38] A. Khosravi, S. Nahavandi, D. Creighton, D. Srinivasan, Interval type-2 fuzzy logic systems for load forecasting: a comparative study, IEEE T. Power Syst., 27 (2012), 1274-1282.
    [39] C. W. Tao, J. S. Taur, C. W. Chang, Y. H. Chang, Simplified type-2 fuzzy sliding controller for wing rocket system, Fuzzy Sets Syst., 207 (2012), 111-129.
    [40] M. A. Sanchez, O. Castillo, J. R. Castro, Generalized type-2 fuzzy systems for controlling a mobile robot and a performance comparison with interval type-2 and type-1 fuzzy systems, Expert Syst. Appl., 42 (2015), 5904-5914.
    [41] L. Cervantes, O. Castillo, Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control, Inform. Sciences, 324 (2015), 247-256.
    [42] O. Castillo, L. Amador-Angulo, J. R. Castro, M. Garcia-Valdez, 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, Inform. Sciences, 354 (2016), 257-274.
    [43] O. Castillo, P. Melin, E. Ontiveros, C. Peraza, P. Ochoa, F. Valdez, J. Soria, A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics, Eng. Appl. Artif. Intel., 85 (2019), 666-680.
    [44] E. Ontiveros-Robles, P. Melin, O. Castillo, Comparative analysis of noise robustness of type 2 fuzzy logic controllers, Kybernetika, 54 (2018), 175-201.
    [45] 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.
    [46] 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.
    [47] Y. Chen, Study on weighted Nagar-Bardini algorithms for centroid type-reduction of general type-2 fuzzy logic systems, J. Intell. Fuzzy Syst., 37 (2019), 6527-6544.
    [48] T. Kumbasar, Revisiting Karnik-Mendel algorithms in the framework of linear fractional programming, Int. J. Approx. Reason., 82 (2017), 1-21.
    [49] Y. Chen, J. X. Wu, J. Lan, Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems, AIMS Math., 5 (2020), 6149-6168.
    [50] S. C. Tong, Y. M. Li, Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties, Science China Information Sciences, 53 (2010), 307-324.
    [51] S. C. Tong, Y. M. Li, Observer-based adaptive fuzzy backstepping control of uncertain pure-feedback systems, Science China Information Sciences, 57 (2014), 1-14.
    [52] Q. F. Fan, T. Wang, Y. Chen, et al, Design and application of interval type-2 fuzzy logic system based on QPSO algorithm, Int. J. Fuzzy Syst., 20 (2018), 835-846.
    [53] M. Deveci, I. Z. Akyurt, S. Yavuz, GIS-based interval type-2 fuzzy set for public bread factory site selection, Journal of Enterprise Information Management, 31 (2018), 820-847.
    [54] L. Liu, Y. J. Liu, S. C. Tong, C. L. P. Chen, Integral barrier Lyapunov function based adaptive control for switched nonlinear systems, Science China Information Sciences, 63 (2020), 1-14.
    [55] L. Liu, Y. J. Liu, D. P. Li, S. C. Tong, Z. S. Wang, Barrier Lyapunov function based adaptive fuzzy FTC for switched systems and its applications to resistance inductance capacitance circuit system, IEEE T. Cybernetics, 50 (2020), 3491-3502.
    [56] F. Chiclana, S. M. Zhou, Type-reduction of general type-2 fuzzy sets: The type-1 OWA approach, Int. J. Intell. Syst., 28 (2013), 505-522.
    [57] J. M. Mendel, H. Hagars, W. W. Tan, W. W. Melek, H. Ying, Introduction to type-2 fuzzy logic control: theory and applications, Wiley-IEEE Press, 2014.
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