In Regular Intervals Fuzzy Model of Linear Regression
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 118-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the fuzzy and ordinary model in the case of simple linear regression is studied. The geometrical interpretation of fuzzy model and its comparing with ordinary model of simple linear regression are given. The computing complexity of fuzzy model of linear regression is investigated. The effective algorithms of the decision having complexity of the orders $O (n\log n) $, $O (n^2) $, and their realization in MatLab are indicated.
Keywords: fuzzy linear regression model, computational complexity.
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I. V. Ponomarev; V. V. Slavsky. In Regular Intervals Fuzzy Model of Linear Regression. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 118-134. http://geodesic.mathdoc.fr/item/VNGU_2010_10_2_a9/

[1] Gmurman V. E., Teoriya veroyatnostei i matematicheskaya statistika, Ucheb. posobie dlya vuzov, 4-e izd., dop., Vyssh. shk., M., 1972 | MR

[2] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR

[3] Preparata F., Sheimos M., Vychislitelnaya geometriya: vvedenie, Mir, M., 1989 | MR | Zbl

[4] Khadviger G., Debrunner G., Kombinatornaya geometriya ploskosti, Nauka, M., 1965 | MR

[5] Barber C. B., Dobkin D. P., Huhdanpaa H. T., “The Quickhull Algorithm for Convex Hulls”, ACM Transactions on Mathematical Software, 22:4, Dec. 1996 (1996), 469–483 | DOI | MR | Zbl

[6] Dug Hun Hong, Changha Hwang, “Support Vector Fuzzy Regression Machines”, Fuzzy Sets Syst., 138:2 (2003), 271–281 | DOI | MR | Zbl

[7] Kyung-Bin Song, Young-Sik Baek, Dug Hun Hong, Gilsoo Jang, “Short-Term Load Forecasting for the Holidays Using Fuzzy Linear Regression Method”, IEEE Transactions on Power Systems, 20:1 (2005), 96–101 | DOI

[8] Lu Jingli, Wang Ruili, “An Enhanced Fuzzy Linear Regression Model with More Flexible Spreads”, Fuzzy Sets Syst., 160:17 (2009), 2505–2523 | DOI | MR | Zbl

[9] Tanaka H., Uejima S., Asai K., “Linear Regression Analysis with Fuzzy Model”, IEEE Transactions on Systems, Man and Cybernetics, 12:6 (1982), 903–907 | DOI | Zbl

[10] Shapiro A. F., “Fuzzy Regression and the Term Structure of Interest Rates Revisited”, Proc. of the $14^\text{th}$ Int. AFIR Colloquium, v. 1, 2004, 29–45