TY - JOUR

T1 - A mathematical programming method for formulating a fuzzy regression model based on distance criterion

AU - Chen, Liang Hsuan

AU - Hsueh, Chan Ching

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007/6

Y1 - 2007/6

N2 - Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several α-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.

AB - Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several α-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.

UR - http://www.scopus.com/inward/record.url?scp=34248994889&partnerID=8YFLogxK

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U2 - 10.1109/TSMCB.2006.889609

DO - 10.1109/TSMCB.2006.889609

M3 - Article

C2 - 17550123

AN - SCOPUS:34248994889

SN - 1083-4419

VL - 37

SP - 705

EP - 712

JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

IS - 3

ER -