Fuzzy least-squares linear regression analysis for fuzzy input-output data. (English) Zbl 1006.62055
Summary: A fuzzy regression model is used in evaluating the functional relationships between the dependent and independent variables in a fuzzy enviromnent. Most fuzzy regression models are considered to be fuzzy outputs and parameters but non-fuzzy (crisp) inputs. In general, there are two approaches in the analysis of fuzzy regression models: linear-programming-based methods and fuzzy least-squares methods. M. Sakawa and H. Yano [Fuzzy Sets Syst. 47, No. 2, 173-181 (1992; Zbl 0751.62030)] considered fuzzy linear regression models with fuzzy outputs, fuzzy parameters and also fuzzy inputs. They formulated multiobjective programming methods for the model estimation along with a linear-programming-based approach. In this paper, two estimation methods along with a fuzzy least-squares approach are proposed. These proposed methods can be effectively used for parameter estimation. Comparisons are also made between them.
MSC:
| 62J05 | Linear regression; mixed models |
| 90C29 | Multi-objective and goal programming |
| 62J99 | Linear inference, regression |
| 90C90 | Applications of mathematical programming |
Keywords:
fuzzy linear regression; estimation; multiobjective programming; fuzzy least-squares; clusterwise regression; noise cluster; robustnessCitations:
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