• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.75-80
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• 1999

As current manufacturing processes require high spindle speed and precise machining, increasing accuracy by reducing volumetric errors of the machine itself, particularly thermal errors, is very important. Thermal errors can be estimated by many empirical models, for example, an FEM model, a neural network model, a linear regression model, an engineering judgment model etc. This paper discusses to make a modeling of thermal errors efficiently through backward elimination and fuzzy logic strategy. The model of a thermal error using fuzzy logic strategy overcome limitation of accuracy in the linear regression model or the engineering judgment model. And this model is compared with the engineering judgment model. It is not necessary complex process such like multi-regression analysis of the engineering judgment model. A fuzzy model does not need to know the characteristics of the plant, and the parameters of the model can be mathematically calculated. Like a regression model, this model can be applied to any machine, but it delivers greater accuracy and robustness.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.507-513
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• 2004

Least-squares support vector machine (LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. In this paper, we propose LS-SVM approach to evaluating fuzzy regression model with multiple crisp inputs and a Gaussian fuzzy output. The proposed algorithm here is model-free method in the sense that we do not need assume the underlying model function. Experimental result is then presented which indicate the performance of this algorithm.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.445-449
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• 2005

Yen et al. [Fuzzy Sets and Systems 106 (1999) 167-177] calculated the fuzzy membership function for the output to find the non-symmetric triangular fuzzy number coefficients of a linear regression model for all given input-output data sets. In this note, we show that the result they obtained in their paper is invalid.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.4
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• pp.366-370
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• 2013

Regression Analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper introduce Theil's method to find a fuzzy regression model which explain the relationship between explanatory variable and response variables. Theil's method is a robust method which is not sensive to outliers. Theil's method use medians of rate of increment based on randomly chosen pairs of each components of ${\alpha}$-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. We propose an example to show Theil's estimator is robust than the Least squares estimator.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.306-311
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• 2008

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.6
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• pp.99-105
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• 1998

This paper is to propose the fuzzy regression model using genetic algorithm which is fuzzy nonlinear regression model. Genetic algorithm is used to classify the input data for better fuzzy regression analysis. From this partition. each data can be have the grade of membership function which is belonged to a divided data group. The data group, from optimal partition of the region of each variable, have different fuzzy parameters of fuzzy linear regression model one another. We compound the fuzzy output of each data group so as to obtain the final fuzzy number for a data. We show the efficiency of this method by means of demonstration of a case study.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.306-310
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• 2008

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.799-813
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• 2008

This paper deals with the properties of the fuzzy least squares estimators for fuzzy linear regression model. Especially fuzzy triangular input-output model including error term is proposed. The error term is considered as a fuzzy random variable. The asymptotic unbiasedness and the consistency of the estimators are proved using a suitable metric.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.6
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• pp.832-836
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• 2008

Fuzzy regression model is used in evaluating relationship between the dependent and independent variables. If linguistic data are obtained, ordinary regression have limitation due to oversimplification of data. In this paper, fuzzy regression model with fuzzy input-output data for estimation of project performance is used.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.