Properties of certain fuzzy linear regression methods. (English) Zbl 0842.62057
Summary: Fuzzy linear regression was originally introduced by H. Tanaka, S. Uejima, and K. Asai [IEEE Trans. Syst. Man. Cybern. 12, 903-907 (1982; Zbl 0501.90060)]. In subsequent years, several different approaches to fuzzy linear regression have been proposed. The purpose of this paper is to review and examine some of these formulations, to discuss their strengths and weaknesses relative to each other, and to suggest possible improvements. In addition, we compare and contrast these methods to the method of ordinary least squares regression.
Keywords:
fuzzy coefficient; fuzzy set; fuzzy logic; fuzzy linear regression; review; ordinary least squares regressionCitations:
Zbl 0501.90060References:
| [1] | Celmins, A., Multidimensional least - squares fitting of fuzzy Models, Mathal Modelling, 9, 669-690 (1987) · Zbl 0636.62111 |
| [2] | Diamond, P., Fuzzy least squares, Information Sciences, 46, 141-157 (1988) · Zbl 0663.65150 |
| [3] | Heshmaty, B.; Kandel, A., Fuzzy linear regression and its applications to forecasting in uncertain events, Fuzzy Sets and Systems, 15, 159-191 (1985) · Zbl 0566.62099 |
| [4] | Hillier, F.; Lieberman, G., Introduction to Operations Research (1990), McGraw-Hill: McGraw-Hill New York · Zbl 0155.28202 |
| [5] | Jo’zsef, S., On the effect of linear data transformation in the possibilistic fuzzy linear regression, Fuzzy Sets and Systems, 45, 185-188 (1992) · Zbl 0745.62074 |
| [6] | Neter, J.; Wasserman, W.; Kutner, M. H., Applied Linear Regression Models (1989), Irwin: Irwin Homewood, Il |
| [7] | 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 |
| [8] | Savic, D.; Pedrycz, W., Evaluation of fuzzy linear regression models, Fuzzy Sets and Systems, 39, 51-63 (1991) · Zbl 0714.62065 |
| [9] | Tanaka, H.; Uegima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybern., 12, 903-907 (1982) · Zbl 0501.90060 |
| [10] | Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems, 24, 363-375 (1987) · Zbl 0633.93060 |
| [11] | Tanaka, H.; Ishibuchi, H., Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters, Fuzzy Sets and Systems, 41, 145-160 (1991) · Zbl 0734.62072 |
| [12] | Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606 |
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.
