Abstract
The paper proposes three fuzzy regression models - concerning temperature and electricity load - based on real data. In the first two models the monthly temperature in a period of four years in a Polish city is analyzed. We assume the temperature to be fuzzy and its dependence on time and on the temperature in the previous month is determined. In the construction of the fuzzy regression models the least square methods was used. In the third model we analyze the dependence of the daily electricity load (assumed to be a fuzzy number) on the (crisp) temperature. Outliers, i.e. non-typical instances in the observations are identified, using a modification of an identification method known from the literature. The proposed method turns out to identify the outliers consistently with the real meaning of the experimental data.
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References
Chanas, S., Nowakowski, M.: Single value simulation of fuzzy variable. Fuzzy Sets and Systems 25, 43–57 (1988)
Chen, Y.S.: Outliers detection and confidence interval modification in fuzzy regression. Fuzzy Sets and Systems 119, 259–272 (2001)
Diamond, P.: Least squares and maximum likelihood regression for fuzzy linear models. In: Kacprzyk, J., Fedrizzi, M. (eds.) Fuzzy Regression Analysis, pp. 137–151. Omnitech Press Warsaw and Physica-Verlag Heidelberg, Warsaw (1992)
Dudois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, San Diego CA (1980)
Gładysz, B.: The electric power load fuzzy regression mode. In: Hryniewicz, O., Kacprzyk, J., Kuchta, D. (eds.) Issues in Soft Computing Decisions of Operations Research, pp. 171–180. Academic Publishing House EXIT, Warsaw (2005)
Gładysz, B., Kuchta, D.: Polynomial least squares fuzzy regression models for temperature. In: Cader, A., Rutkowski, L., Tadeusiewicz, R., Zurada, J. (eds.) Artificial Intelligence and Soft Computing, pp. 118–124. Academic Publishing House EXIT, Warsaw (2006)
Nasrabadi, M.M., Nasrabadi, E., Nasrabadi, A.R.: Fuzzy linear regression analysis: A multi-objective programming approach. Applied Mathematics and Computation 163, 245–251 (2005)
Nazarko, M., Zalewski, W.: The fuzzy regression approach to peak load estimation in power distribution systems. IEEE Transactions on Powr Systems 8(3), 809–814 (1999)
Özelkan, E.C., Duckstein, L.: Multi-objective fuzzy regression: a general framework. Computers and Operations Research 27, 635–652 (2000)
Sakawa, M., Yano, H.: Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets and Systems 47, 173–181 (1992)
Shen, R.: Fuzzy causal relation analysis in time series. In: Kacprzyk J., Fedrizzi M. (eds.) Fuzzy Regression Analysis, Omnitech Press Warsaw and Physica-Verlag Heilderberg, Warsaw, pp. 181–193 (1992)
Statistic Annuals. Regional Statistical Office, Wrocław (2000-2004)
D’Urso, P., Gastaldi, T.: An ordewise polynomial regression procedure for fuzzy data. Fuzzy Sets and Systems 130, 1–19 (2002)
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Gładysz, B., Kuchta, D. (2007). Outliers Detection in Selected Fuzzy Regression Models. In: Masulli, F., Mitra, S., Pasi, G. (eds) Applications of Fuzzy Sets Theory. WILF 2007. Lecture Notes in Computer Science(), vol 4578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73400-0_26
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DOI: https://doi.org/10.1007/978-3-540-73400-0_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73399-7
Online ISBN: 978-3-540-73400-0
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