Design of a robust interval-valued type-2 fuzzy c-regression model for a nonlinear system with noise and outliers. (English) Zbl 07094616
Summary: This paper presents the development of a novel interval-valued type-2 robust fuzzy c-regression model (IVT2RFCRM) clustering algorithm for identification of nonlinear systems taking into account the presence of noise and outliers in the associated dataset. On the one hand, the proposed method allows for the handling of the uncertainties of the FCRM due to its fixed fuzzier parameter \(m\). On the other hand, the dataset is subject to various sources of uncertainty such as measurement uncertainty, fuzziness of information and environmental noise. As a result, obtaining a high-quality approximation of real processes is often a difficult task. In this paper, the structure of the proposed clustering algorithm is given and its parameter update rule is derived. First, the modified objective functions use a kernel measure of error to deal with the noisy data. Then, a credibility function is integrated into the clustering process in order to reduce the effect of outliers. Finally, the effectiveness of the proposed algorithm is evaluated by comparing the obtained results with others reported in the literature and also through the simulation results of a real liquid level process.
MSC:
| 62J86 | Fuzziness, and linear inference and regression |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62H86 | Multivariate analysis and fuzziness |
Keywords:
type-2 fuzzy systems; identification; fuzzy c-regression model; kernel approach; noise clustering; credibility functionReferences:
| [1] | Bernardo D, Hagras H, Tsang E (2013) A genetic type-2 fuzzy logic based system for the generation of summarised linguistic predictive models for financial applications. Soft Comput 17(12):2185-2201 |
| [2] | Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York · Zbl 0503.68069 |
| [3] | Bhattacharya D, Konar A (2017) Self-adaptive type-1/type-2 hybrid fuzzy reasoning techniques for two-factored stock index time-series prediction. Soft Comput 21:1-18 |
| [4] | Billings S, Voon W (1986) Correlation based model validity tests for non-linear models. Int J Control 44(1):235-244 · Zbl 0589.93066 |
| [5] | Billings S, Zhu Q (1994) Nonlinear model validation using correlation tests. Int J Control 60(6):1107-1120 · Zbl 0813.93012 |
| [6] | Chaoshun L, Jianzhong Z, Xiuqiao X, Qingqing L, Xueli A (2009) T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm. Eng Appl Artif Intell 22(4-5):646-653 |
| [7] | Chaoshun L, Jianzhong Z, Xiuqiao X, Qingqing L, Xueli A (2010) A new T-S fuzzy-modeling identification approach to identify a boiler-turbine. Expert Syst Appl 37(3):2214-2221 |
| [8] | Chaoshun L, Jianzhong Z, BO F, Pangao K, Jian X (2012) T-S fuzzy model identification with a gravitational search-based hyperplane clustering algorithm. IEEE Trans Fuzzy Syst 20(2):305-317 |
| [9] | Chen JQ, Xi YG, Zhang ZJ (1998) A clustering algorithm for fuzzy model identification. Fuzzy Sets Syst 98(3):319-329 |
| [10] | Chen Y, Wang D, Tong S (2016) Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: with the combination of BP algorithms and KM algorithms. Neurocomputing 174:1133-1146 |
| [11] | Chintalapudi KK, Kam M (1998a) A noise resistant fuzzy c-means algorithm for clustering. In: IEEE conference on fuzzy systems proceedings, Anchorage, AK, vol. 2, pp 1458-1463 |
| [12] | Chintalapudi KK, Kam M (1998b) A noise-resistant fuzzy c-means algorithm for clustering. In: IEEE international conference on fuzzy systems proceedings, vol 2, pp 1458-1463 |
| [13] | Chuang CC, Su SF, Chen SS (2001) Robust tsk fuzzy modeling for function approximation with outliers. IEEE Trans Fuzzy Syst 9(6):810-821 |
| [14] | Chuang CC, Hsiao CC, Jeng JT (2003) Adaptive fuzzy regression clustering algorithm for TSK fuzzy modeling. In: IEEE international symposium on computational intelligence in robotics and automation, vol 1, pp 201-206 |
| [15] | Chuang CC, Jeng JT, Tao CW (2009) Hybrid robust approach for tsk fuzzy modeling with outliers. Expert Syst Appl 36:8925-8931 |
| [16] | Cunyong Q, Jian X, Long Y, Lu H, Muhammad NI (2013) A modified interval type-2 fuzzy c-means algorithm with application in mr image segmentation. Pattern Recogn Lett 34:1329-1338 |
| [17] | Dave RN (1991) Characterization and detection of noise in clustering. Pattern Recogn Lett 12(11):657-664 |
| [18] | Dave RN, Krishnapuram R (1997) Robust clustering methods: a unified view. IEEE Trans Fuzzy Syst 5(2):270-293 |
| [19] | Dave RN, Sumit S (2002) Robust fuzzy clustering of relational data. IEEE Trans Fuzzy Syst 10(6):713-727 |
| [20] | Graves D, Pedrycz W (2010) Kernel-based fuzzy clustering and fuzzy clustering: a comparative experimental study. Fuzzy Sets Syst 161(4):522-543 |
| [21] | Gustafson DE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE conference on decision control, Piscataway, NJ, USA, pp 761-766 · Zbl 0448.62045 |
| [22] | Harish BS, Kumar SVA (2017) Anomaly based intrusion detection using modified fuzzy clustering. Int J Interact Multimed Artif Intell 4(6):54-59 (Regular Issue) |
| [23] | Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1(3):195-204 |
| [24] | Hwang C, Rhee F (2007) Uncertain fuzzy clustering: interval type-2 fuzzy approach to c-means. IEEE Trans Fuzzy Syst 15(1):107-120 |
| [25] | Kaur P, Gosain A (2011) A density oriented fuzzy c-means clustering algorithm for recognising original cluster shapes from noisy data. Int J Innov Comput Appl 3(2):77-87 |
| [26] | Kaura P, Sonib AK, Gosainc A (2013) Robust kernelized approach to clustering by incorporating new distance measure. Eng Appl Artif Intell 26(2):833-847 |
| [27] | Kim E, Park M, Ji S, Park M (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 5(3):328-337 |
| [28] | Kim E, Park M, Kim S, Park M (1998) A transformed input-domain approach to fuzzy modeling. IEEE Trans Fuzzy Syst 6(4):596-604 |
| [29] | Kung CC, Su JY (2007) Affine Takagi-Sugeno fuzzy modelling algorithm by fuzzy c-regression models clustering with a novel cluster validity criterion. IET Control Theory Appl 1(5):1255-1265 |
| [30] | Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice-Hall, Upper Saddle River · Zbl 0978.03019 |
| [31] | Nie M, Tan WW (2008) Towards an efficient type-reduction method for interval type-2 fuzzy logic systems. In: 2008 IEEE international conference on fuzzy systems (ieee world congress on computational intelligence) pp 1425-1432. https://doi.org/10.1109/FUZZY.2008.4630559 |
| [32] | Ondrej L, Milos M (2012) General type-2 fuzzy c-means algorithm for uncertain fuzzy clustering. IEEE Trans Fuzzy Syst 20(5):883-897 |
| [33] | Qun R, Marek B, Luc B (2012) High-order interval type-2 Takagi-Sugeno-Kang fuzzy logic system and its application in acoustic emission signal modeling in turning process. Int J Adv Manuf Technol 63(9-12):1057-1063 |
| [34] | Rahib H, Okyay K, Tayseer A, Fakhreddin M (2011) A type-2 neuro-fuzzy system based on clustering and gradient techniques applied to system identification and channel equalization. Appl Soft Comput 11(1):1396-1406 |
| [35] | Rehm F, Klawonn F, Kruse R (2007) A novel approach to noise clustering for outlier detection. Soft Comput 11(5):489-494 |
| [36] | Soltani M, Chaari A (2015) A pso-based fuzzy c-regression model applied to nonlinear data modeling. Int J Uncertain Fuzziness Knowl Based Syst 23(06):881-891 |
| [37] | Soltani M, Chaari A, BenHmida F (2012) A novel fuzzy c-regression model algorithm using new measure of error and based on particle swarm optimization. Int J Appl Math Comput Sci 22(3):617-628 · Zbl 1305.93211 |
| [38] | Soltani M, Chaari A (2013) Fuzzy c-regression models based on euclidean particle swarm optimization in noisy environment. In: International conference on control, decision and information technologies, Hammamet, Tunisia, pp 585-589 |
| [39] | Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116-132 · Zbl 0576.93021 |
| [40] | Yang MS, Tsai HS (2008) A gaussian kernel-based fuzzy c-means algorithm with a spatial bias correction. Pattern Recogn Lett 29(12):1713-1725 |
| [41] | Yinga KC, Lin SW, Lee ZJ, Leec IL (2011) A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization. Appl Soft Comput 11(2):1820-1826 |
| [42] | Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning. Inf Sci 8(3):199-249 · Zbl 0397.68071 |
| [43] | Zang X, Vista FP, Chong K (2014) Fast global kernel fuzzy c-means clustering algorithm for consonant/vowel segmentation of speech signal. J Zhejiang Univ Sci C 15(7):551-563 |
| [44] | Zarandi MF, Gamasaee R (2013) A type-2 fuzzy system model for reducing bullwhip effects in supply chains and its application in steel manufacturing. Sci Iran 20(3):879-899 |
| [45] | Zarandi M, Gamasaee R, Turksen I (2012) A type-2 fuzzy c-regression clustering algorithm for Takagi-S system identification and its application in the steel industry. Inf Sci 187:179-203 |
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