A method of variable selection for fuzzy regression – the possibility approach

• Authors: Barbara GŁADYSZ , Dorota KUCHTA
• Languages of publication: EN

Abstracts

EN

A method of variable selection for fuzzy regression has been proposed. Using the method, the significance of fuzzy regression coefficients has been examined. The method presented is equivalent to the method of variable selection for classical regression based on an analysis of the confidence intervals for their coefficients. Illustrative examples are presented.

Keywords

EN

fuzzy regression; possibility distribution of a fuzzy variable; variable significance

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2011
• Volume: 21
• Issue: 2
• Pages: 5-15

Contributors

author

Barbara GŁADYSZ

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

author

Dorota KUCHTA

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

References

• DUBOIS D., PRADE H., Possibility Theory, An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.
• CELMINS A., Multidimensional least-squares fitting of fuzzy models. Mathematical Modelling, 1987, 9, 669–690.
• DIAMOND P., Fuzzy least squares, Information Sciences, 1988, 46, 141–157.
• D’URSO P., GASTALDI T., An “ordewise” polynomial regression procedure for fuzzy data, Fuzzy Sets and Systems, 2002, 130, 1–19.
• D’URSO P., SANTARO A., Goodness of fit and variable selection in fuzzy regression multiple linear regression, Fuzzy Sets and Systems, 2006, 157 (19), 2627–2647.
• GŁADYSZ B., Interval and Fuzzy Regression, PWN, Warsaw, 2011 (in Polish).
• GŁADYSZ B., KUCHTA D., Least squares method for L-R fuzzy variables, W.V. Di Gesu, S.K. Pal, A. Petrosino (Eds.), Lecture Notes in Computer Science, Lecture Notes in Artificial Inteligence, LNAI, 2009, 5571, 36–43.
• KACPRZYK J., FEDRIZZI M., Fuzzy Regression Analysis, Omnitech Press Warsaw, and Physica Heilderberg, 1992.
• KÖRNER R., NÄTHER W., Linear regression with random fuzzy variables. Extended classical estimates, bestlinear estimates, least squares estimates, Information Sciences, 1998, 109, 95–118.
• MADDALA G.S., Introduction to Econometrics, Wiley, 2001.
• SAKAWA M., YANO H., Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 1992, 47, 173–181.
• SAVIC D.A., PEDRYCZ W., Evaluation of fuzzy linear regression modes, Fuzzy Sets and Systems, 1991, 23, 51–63.
• TROSKA M., Econometric modelling of cost drivers in the activity based costing, PhD Thesis, Wroclaw University of Technology, Wroclaw, 2009 (in Polish).
• WANG H.-F., TSUAR R.-CH., Bicriteria variable selection in a fuzzy regression equation, Computers & Mathematics with Applications, 2000, 40 (6–7), 877–883.
• ZADEH L.A., Fuzzy Sets, Information and Control, l8, 1965, 338–353.
• ZADEH L.A., Fuzzy sets as a basis of theory of possibility, Fuzzy Sets and Systems, 1978, 1, 3–28