school
Macau Periodical Index (澳門期刊論文索引)
- Author
- Chan, Lai Kow; Wu, Ming Lu
- Title
- Fuzzy regression: methods and evaluations
- Journal Name
- 澳門科技大學學報
- Pub. Info
- Jun. 2007, Vol.1, No.1, pp. 46-62
- Keyword
- fuzzy distance；fuzzy regression；least squares method；linear programmming；multi-objective programming；nonlinear programming；possibilistic constraints；triangular fuzzy numbers
- Abstract
- Abstract : Fuzzy regression has experienced fast development in the past two decades as an alternative to model vague phenomena and subjective data for which traditional statistical regression may be ineffective. To facilitate practitioners' easy understandings and appropriate selections for use, this paper provides a brief review and comprehensive evaluation of various fuzzy possibilisitc regression(FPR) odels, fuzzy necessity and conjunction regression methods and FPR models with quadratic and exponential membership membership functions, Celmins's and Diamond's fuzzy least squares methods, Savic and Pedryzc's two- stage fuzzy regression approach, Sakawa and Yano's as well as Ozelkan and Duckstein's multi-objective fuzzy regression models, and peters' fuzzy regression method is firest precisely presented, from which computational procedures can easily be established for practitioners to estimate and analyze the corresponding fuzzy regression model. the strengths and weaknesses of the various fuzzy regression methods are then systematically assessed based on the relevant literature, and the comparatively simple and reliable two-stage fuzzy regression method is tentatively recommended for practitioners to use in fuzzy modeling. Ten influential and representative fuzzy regression pubications are finally suggested for the easy and quick references of interested readers, especially for those who are not yet very familiar with fuzzy regression. Paragraph Headings： 1. Fuzzy regression vs statistical regression 1.1. Statistical regression 1.2. Fuzzy regression as compared to statistical 1.3. About this paper 2. Overview of fuzzy regression methods 2.1. Fuzzy possibilistic regression methods 2.2. Fuzzy necessity and conjunction regression methods 2.3. FPR models with quadratic/exponential membership functions 2.4. Fuzzy least squares regression: Celmins's methods 2.5. Fuzzy least squares regression: Diamond's methods 2.6. Two-stage fuzzy regression methods 2.7. Fuzzy LP based FPR methods 2.8. Multi-objective fuzzy regression methods 3. Evaluation of fuzzy regression methods 3.1. Fuzzy possibilistic regression methods 3.2. Fuzzy necessity and conjunction regression methods 3.3. FPR methods with quadratic/exponential membership functions 3.4. Fuzzy least squares regression: Celmins's methods 3.5. Fuzzy least squares regression: Diamond's methods 3.6. Two- stage fuzzy regression method 3.7. Fuzzy LP based FPR method 3.8. Multi-objective fuzzy regression methods 4. Concluding remarks