Parameter Estimation Based Type-II Fuzzy Logic and Comparison with Robust Methods

Parameter estimation is one of the important stages of regression analysis. In the regression analysis, while parameter estimation by classical methods there are a number of assumptions need to be satisfied. One of them is error are normally distributed. In the case that the data sets have outliers, providing of this assumption becomes more difficult. When a data set has outliers, robust methods such as the M method (Huber, Hampel, Andrews and Tukey) are used for estimating parameters. In this paper the Adaptive Network Based Fuzzy Inference System (ANFIS) is used to parameter estimation which is the neural network architecture based type-II fuzzy logic. The proposed method has the properties of a robust method, because the process does not give permission to the intuitional and is not affected by the outliers. Consequently, another aim of this study is, to compare the proposed method with the robust methods that are mentioned above.

Keywords:

Type-II fuzzy logic, outliers robust regression, membership function,

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[1] Aisbett, J.,Rickart, J. T., Morgenthaler, D., Multivariate modeling and type-2 fuzzy sets, Fuzzy Sets and Systems 163 (2011) 78-95.
[2]Castillo, O., Melin, P. Type-2 fuzzylogic: theory and applications, Sipringer, 2008.
[3] Cheng, C.B., Lee, E.S., Switching Regression Analysis by Fuzzy Adaptive Network, Europen Journal of Operational Research 128, (2001) 647-668.
[3]Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A., Robust Statistics, John- Willey and Sons, New-York (1986).
[5]Hisao, I., Manabu, N., Fuzzy Regression Usin Asymmetric Fuzzy Coefficients and Fuzzied Neural Networks, Fuzzy Sets and Systems 119 (2001) 273-290.
[6]Hogg, R.V. Statistician robustness: One View of Its Use in Applications Today. The American Statistician, 33, (1979) 108-115.
[7]Huber, P.J., Robust statistics. John Willey and Son (1981).
[8]Huynh, H., A Comparison of For Approaches to Robust Regression, Psychological Bulletin, 92, (1982) 505-512.
[9]Karnik N.K.,Mendel, J.M.,Type-2 Fuzzy logic systems, IEEE Transaction on Fuzzy Systems 7 (1999) 643-658.
[10]Karnik N.K.,Mendel, J.M., Centroid of a type-2 fuzzy set, Information Sciences 132 (2001) 195-220.
[11]Kula, K.S.and Apaydn, A., Fuzzy robust regression analaysis based on the ranking of fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16,(2008) 663-681.
[12]Kula, K. S., Dalkilic, T. E., Parameter Estimation Based Type-II Fuzzy Logic, TWMS J. Pure Appl. Math, 4-2, (2013) 187-193.
[13] Mendel, J.M., John, R.I.B., Type-2 fuzzy sets made simple, IEEE Transaction on Fuzzy Systems 10 (2002) 117-127.
[14]Mendel, J. M.,Type-2 Fuzzy Sets and Systems: An Overview, IEEE Computational Intelligence Magazine Fabuary (2007) 21-29.
[15]Mendel, J. M.,Advances in type-2 fuzzy sets and systems, Information Sciences 177 (2007) 84-110.
[16]Rousseeuw, P.J, Leroy, A.M., Robust regression and outlier detection. John Willey and Son, (1987).
[17]Türkşen, I.B., Type I and Type II fuzzy systems modelling, Fuzzy Sets and Systems 106 (1999) 11-34.
[18]Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning-1,Information Science 8 (1975) 199-249.

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

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