Insight of a fuzzy regression model. (English) Zbl 0948.62050
Summary: Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise, and variables are interacting in an uncertain, qualitative, and fuzzy way. Thus, it may have considerably practical applications in many management and engineering problems. But there is still lack of proper interpretation about fuzzy regression. We provide an insight into regression intervals so that regression interval analysis, data type analysis and variable selections can be analytically performed. Numerical examples are provided for illustration.
MSC:
| 62J05 | Linear regression; mixed models |
| 62J99 | Linear inference, regression |
| 62G99 | Nonparametric inference |
Keywords:
fuzzy linear regression; intrinsically linear; SST; SSR; SSE; IC; partial IC; forward selectionReferences:
| [1] | Chatterjee, S.; Price, B., Regression Analysis by Example (1991), Wiley: Wiley New York |
| [2] | Cox, D. R.; Shell, E. J., The choice of variables in observational studies, Appl. Statist., 23, 51-59 (1974) |
| [3] | Kacprzyk, J.; Fedrizzi, M., Fuzzy Regression Analysis (1992), Physica-Verlag: Physica-Verlag Heidelberg · Zbl 0758.00005 |
| [4] | Kim, K. J.; Moskowitz, H.; Koksalan, M., Fuzzy versus statistical linear regression, European J. Oper. Res., 92, 417-434 (1996) · Zbl 0912.90064 |
| [5] | Montgomery, D. C.; Peck, E. A., Introduction to Linear Regression Analysis (1982), Wiley: Wiley New York · Zbl 0587.62134 |
| [6] | Moskowitz, H.; Kim, K., On assessing the \(h\) value in fuzzy linear regression, Fuzzy Sets and Systems, 58, 303-327 (1993) · Zbl 0791.62073 |
| [7] | Pedrycz, W.; Savic, D. A., Evaluation of fuzzy regression models, Fuzzy Sets and Systems, 39, 51-63 (1991) · Zbl 0714.62065 |
| [8] | Peters, G., Fuzzy linear regression with fuzzy intervals, Fuzzy Sets and Systems, 63, 45-55 (1994) |
| [9] | Redden, D. T.; Woodall, W. H., Further examination of fuzzy linear regression, Fuzzy Sets and Systems, 79, 203-211 (1996) |
| [10] | Sakawa, M.; Yano, H., Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 47, 173-181 (1992) · Zbl 0751.62030 |
| [11] | Talreja, R., Fatigue of Composite Materials (1987), Technomic Publishing Company: Technomic Publishing Company Pennsylvania · Zbl 0561.73090 |
| [12] | Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems, 24, 363-375 (1987) · Zbl 0633.93060 |
| [13] | Tanaka, H.; Uejima, S.; Asai, K., Fuzzy linear model, fuzzy linear regression model, IEEE Trans. System Man Cybernet., 12, 903-907 (1982) · Zbl 0501.90060 |
| [14] | Tanaka, H.; Watada, J., Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets and Systems, 27, 275-289 (1988) · Zbl 0662.93066 |
| [15] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning I, Inform. Sci., 8, 199-249 (1975) · Zbl 0397.68071 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
