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

Liang Hsuan Chen, Chan Ching Hsueh

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)705-712
Number of pages8
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Issue number3
Publication statusPublished - 2007 Jun

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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