UDC 510.644
FULLY FUZZY REGRESSION INADEQUATE OLS ESTIMATORS CORRECTION VIA ROTATION TRANSFORMATIONS
K. V. Bukhensky, Ph.D. (Phys. and Math.), associate professor, Head of the Department of Higher Mathematics, RSREU, Ryazan, Russia; orcid.org/0000-0003-2602-2112, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. N. Konyukhov, Ph.D. (Ped. Sc.), associate professor, RSREU, Ryazan, Russia;
orcid.org/0000-0002-1523-7110, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. B. Dubois, Ph.D. (Phys. and Math.), associate professor, RSREU, Ryazan, Russia;
orcid.org/0000-0002-5924-4128, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
D. O. Popova, fourth year student, Faculty of Engineering and Economics, RSREU, Ryazan, Russia;
orcid.org/0009-0002-0539-8540, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
S. S. Semina, third year student, Faculty of Automatics and Information Technologies in Сontrol, RSREU, Ryazan, Russia;
orcid.org/0000-0002-8820-5806, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The aim of the work is to apply rotation transformations for the correction of inadequate OLS estimators of single factor fully fuzzy regression (FFR). In this paper the estimator is supposed to be inadequate if at least one of the following takes place: 1) fuzzy slope has no particular sign; 2) fuzzy slope or intercept are non-convex fuzzy sets (FSs); 3) negative spreads occur. The first case means violation of calculation assumptions made a priori. Two subsequent cases are in contradiction to fuzzy numbers (FNs) axioms. The method proposed includes the analysis of FFR’s coefficients of α-cut OLS estimators for the inadequacies mentioned above and their removal via rotation transformations of different coordinate planes in sixdimensional structural parameter space of input and output variables, being triangular FNs (two modal values and four spreads). The numerical experiments show that the technique proposed ensures empirical and predicted FNs shape functions identity and leads to significant approximation root mean square error (RMSE) drop calculated in original conditions.
Key words: : fuzzy set, LR-type fuzzy number, membership function, shape function, α-cut, fully fuzzy regression, α-cut ordinary least squares.