General fuzzy piecewise regression analysis with automatic change-point detection

Yu et al. (Fuzzy Sets and Systems 105 (1999) 429) performed general piecewi se necessity regression analysis based on linear programming (LP) to obtain the necessity area. Their method is the same as that according to data dis tribution, even if the data are irregular, practitioners must specify the n umber and the positions of change-points. However, as the sample size incre ases, the number of change-points increases and the piecewise linear interv al model also becomes complex. Therefore, this work devises general fuzzy p iecewise regression analysis with automatic change-point detection to simul taneously obtain the fuzzy regression model and the positions of change-poi nts. Fuzzy piecewise possibility and necessity regression models are employ ed when the function behaves differently in different parts of the range of crisp input variables. As stated, the above problem can be formulated as a mixed-integer programming problem. The proposed fuzzy piecewise regression method has three advantages: (a) Previously specifying the number of chang e-points, then the positions of change-points and the fuzzy piecewise regre ssion model are obtained simultaneously. (b) It is more robust than convent ional fuzzy regression. The conventional regression is sensitive to outlier s. In contrast, utilizing piecewise concept, the proposed method can deal w ith outliers by automatically segmenting the data. (c) By employing the mix ed integer programming, the solution is the global optimal rather than loca l optimal solution. For illustrating more detail, two numerical examples ar e shown in this paper. By using the proposed method, the fuzzy piecewise re gression model with detecting change-points can be derived simultaneously. (C) 2001 Elsevier Science B.V. All rights reserved.