Fuzzy Sets and Systems 119 (2001) 247–257 www.elsevier.com/locate/fss General fuzzy piecewise regression analysis with automatic change-point detection Jing-Rung Yu a ; ∗ , Gwo-Hshiung Tzeng b , Han-Lin Li a a Institute of Information Management, College of Management, National Chiao Tung University, Hsinchu 30050, Taiwan b Energy and Environmental Research Group, Institute of Trac and Transportation, and Institute of Information Management, College of Management, National Chiao Tung University, 114, 4F, Chung Hsiao W. Rd., Taipei 100, Taiwan Received September 1997; received in revised form August 1998 Abstract Yu et al. (Fuzzy Sets and Systems 105 (1999) 429) performed general piecewise necessity regression analysis based on linear programming (LP) to obtain the necessity area. Their method is the same as that according to data distribution, even if the data are irregular, practitioners must specify the number and the positions of change-points. However, as the sample size increases, the number of change-points increases and the piecewise linear interval model also becomes complex. Therefore, this work devises general fuzzy piecewise regression analysis with automatic change-point detection to simultaneously obtain the fuzzy regression model and the positions of change-points. Fuzzy piecewise possibility and necessity regression models are employed when the function behaves dierently in dierent 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 change-points, then the positions of change-points and the fuzzy piecewise regression model are obtained simultaneously. (b) It is more robust than conventional fuzzy regression. The conventional regression is sensitive to outliers. In contrast, utilizing piecewise concept, the proposed method can deal with outliers by automatically segmenting the data. (c) By employing the mixed integer programming, the solution is the global optimal rather than local optimal solution. For illustrating more detail, two numerical examples are shown in this paper. By using the proposed method, the fuzzy piecewise regression model with detecting change-points can be derived simultaneously. c  2001 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy regression; Piecewise regression; Change-point; Possibility; Necessity 1. Introduction In the early 1980s, Tanaka et al. [8] introduced a linear programming (LP) based regression method using a linear fuzzy model with symmetrical triangular fuzzy parameters. Then the possibility and necessity analyses were clearly dened [5]. Recently, Sakawa and Yano [2,3] have generalized the minimization, maximization and conjunction formulation that were developed by Tanaka [5] and Tanaka et al. [6]. * Corresponding author. Tel.: +886 35 728 709; fax: +886 35 723 792. 0165-0114/01/$ - see front matter c  2001 Elsevier Science B.V. All rights reserved. PII: S0165-0114(98)00384-4