Outliers detection method in fuzzy regression

• Autorzy: Gładysz B.
• Języki publikacji: EN

Abstrakty

EN

In this article we propose a method for identifying outliers in fuzzy regression. Outliers in a sample may have an important influence on the form of the regression equation. For this reason there is great scientific interest in this issue. The method presented is analogous to the method of finding outliers based on the studentized distribution of residuals. In order to identify outliers, regression models are constructed with an additional explanatory variable for each observation. Next, the significance of a fuzzy regression coefficient is analysed considering this additional explanatory variable. Illustrative examples are presented.

Słowa kluczowe

EN

fuzzy regression; outliers; possibility theory

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2010
• Tom: Vol. 20, No. 2
• Strony: 26--39
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Gładysz B.

• Institute of Organization and Management, Department of Management, Wrocław University of Technology, ul. Smoluchowskiego 25, 50-372 Wrocław,

Bibliografia

• [1] DUBOIS D., PRADE H., Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press New York, 1988.
• [2] GŁADYSZ B., KUCHTA D., Multi criteria programming in robust estimation for interval data, Foundation of Computing and Decision Sciences, 2008, 33 (2), 193–207.
• [3] HUBER P.J., Robust statistics, John Wiley & Sons, Hoboken, New Jersey, 2004.
• [4] KACPRZYK J., FEDRIZZI M., Fuzzy Regression Analysis, Omnitech Press Warsaw and Physica-Verlag Heilderberg, Warsaw, 1992.
• [5] MADDALA G.S., Ekonometria, PWN, Warszawa, 2006.
• [6] NASRABADI M.M., NASRABADI E., NASRABADI A.R., Fuzzy linear regression analysis: A multiobjective programming approach, Applied Mathematics and Computation, 2005, 163, 245–251.
• [7] ÖZELKAN E.C., DUCKSTEIN L., Multi-objective fuzzy regression: a general framework, Computers and Operation Research, 2002, 27, 635–652.
• [8] PETERS G., Fuzzy linear regression with fuzzy intervals, Fuzzy Sets and Systems, 1994, 63, 45–55.
• [9] ROUSSEEUW P., LEROY A.M., Robust regression and outlier detection, John Wiley & Sons, 1987.
• [10] SAKAWA M., YANO H., Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 1992, 47, 173–181.
• [11] TANAKA H., UEJIMA S., ASAI K., Linear regression analysis with fuzzy model, IEEE Transaction on Systems Man and Cybernetics, 1982, 12, 903–907.
• [12] ZADEH L.A., Fuzzy Sets, Information and Control, 1965, (8), 338–353.
• [13] ZADEH L.A., Fuzzy sets as a basis of theory of possibility, Fuzzy Sets and Systems, 1978, (1), 3–28.