Parameter estimation by type-2 fuzzy logic in case that data set has outlier

Year 2020, Volume: 69 Issue: 2, 1193 - 1204, 31.12.2020

Türkan Erbay Dalkılıç , Kamile Şanlı Kula , Seda Sağırkaya Tolan

https://doi.org/10.31801/cfsuasmas.713755

Abstract

One of the problems encountered in estimating the unknown parameters of the regression models is the presence of outliers in the data set. This situation may cause problems in providing some assumptions such as the normal distribution for the parameter estimation process and the homogeneity of the variances. The case of the presence of outlier observations in the data set, estimation methods based on fuzzy logic that can be minimized the level of impact of this data are emerged as available methods. If fuzzy logic is used in regression analysis, there are two main steps for parameter estimation. The first of these is to define the clusters that compose the data set, and the other is calculate the degree of membership to determining the contributions of the data to each model for the clusters. In this study, type-2 fuzzy clustering algorithm defined as an expansion of fuzzy c-means algorithm in the determination of membership degrees of data sets was benefited. The presence of outliers in the data set is addressed. An algorithm has been proposed to estimate the unknown belonging to parameters of the regression model using the membership degrees obtained relating to the cluster elements. The parameters were estimated using regression methods to examine the effectiveness of the algorithm that called robust methods, and the results obtained were compared.

Keywords

Type-2 Fuzzy Clustering, Parameter Estimate, Outliers, timate Outliers

References

• Zadeh, L. A., Fuzzy Sets, Information and Control, 8 (1965), 338-353.
• Dunn, J. C., A Fuzzy Relative of ISODATA Process and its Use in Detecting Compact Well-Separated Clusters, Journal of Cybernetics, 3 (1973), 32-57.
• Zadeh, L. A., Fu, K., Tanaka K. and Shimura, M., Fuzzy Sets and Their Applications to Cognitive and Decision Processes, 1975.
• Bezdek, J. C., Ehrlich, R. and Full, W., FCM: The fuzzy C-means clustering algorithm, Computers and Geosciences, 10 (1984), 191-203.
• Mendel, J. and John, R. I., Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy Systems, 10(2) (2002), 117-127.
• Hwang C. and Rhee, F., Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-means, IEEE Transactions on Fuzzy Systems, 15(1) (2007), 107-120.
• Dalkilic, E. T. and Apaydin,A., A fuzzy adaptive network approach to parameter estimation in cases where independent variable come from an exponential distribution, Journal of Computational and Applied Mathematics, 233, (2009), 36-45.
• Juang, C. F., Huang, R. B. and Lin, Y. Y., A recurrent self-evolving interval type-2 fuzzy neural network for dynamic system processing, IEEE Trans. Fuzzy Syst., 17 (2009), 1092-1105.
• Fazel Zarandi, M. H., Turksen, I. B. and Gamasaee, R., A type-2 fuzzy C-regression clustering algorithm for Takagi-Sugeno system identification and its application in the steel industry, Inform. Sci., 187 (2012), 179-203.
• Enke, D. and Mehdiyew, N., Type-2 fuzzy clustering and type-2 fuzzy inference neural network for the prediction of short-term interest rates, Procedia Computer Science, 20 (2013), 115-120.
• Kalhori, M. R. N. and Fazel Zarandi, M. H., Interval type-2 credibilistic clustering for pattern recognition, Pattern Recognition, 48 (2015), 3652-3672 .
• Golsefid, S. M. M. and Zarandi, M. H. F., Dual-centers type-2 fuzzy clustering framework and its verification and validation indices, Applied Soft Computing, 47 (2016), 600-613.
• Hwak, K. C., A design of incremental granular model using context-based interval type-2 fuzzy C-means algorithm, IEICE Trans. Inf. and Syst., E99-D (1) (2016), 309-312.
• Rubio, E., Castillo, O., Valdez, F., Melin, P., Gonzalez, C. and Martinez, G., An extension of the fuzzy possibilistic clustering algorithm using type-2 fuzzy logic techniques, Adv. Fuzzy Systems, 2017 (23) (2017).
• Mendel, J., Computing derivatives in interval type-2 fuzzy logic systems, IEEE Trans. Fuzzy Syst., 12(1) (2004), 84-98.
• Rhee, F. and Hwang, C., A type-2 fuzzy C-means clustering algorithm, in Proc. Joint Conf. IFSA/NAFIPS, (2001), 1926-1919.
• Karnik, N. N. and Mendel, J. M., Type-2 fuzzy logic systems: type-reduction, in IEEE Systems, Man, Cybernet Conference, San Diego, CA, (1998).
• Rousseeuw, P.J and Leroy, A.M., Robust regression and outlier detection. John Willey and Son, 1987.
• Huynh, H. A., Comparison of For Approaches to Robust Regression, Psychological Bulletin, 92 (1982), 505-512.
• Huber, P.J., Robust statistics. John Willey and Son, 1981.
• Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A., Robust Statistics, John- Willey and Sons, New-York, 1986.