• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.591-601
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• 2005

The results of fuzzy linear regression are very sensitive to irregular data. When this points exist in a set of data, a fuzzy linear regression model can be incorrectly interpreted. The purpose of this paper is to detect irregular data and to propose robust fuzzy linear regression based on M-estimators with triangular fuzzy regression coefficients for crisp input-output data. Numerical example shows that irregular data can be detected by using the residuals based on M-estimators, and the proposed robust fuzzy linear regression is very resistant to this points.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.515-524
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• 2007

This paper deals with local linear estimation of fuzzy regression models based on Diamond(1998) as a new class of non-linear fuzzy regression. The purpose of this paper is to introduce a use of smoothing in testing for lack of fit of parametric fuzzy regression models.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.319-325
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• 2001

In this note, we propose a simple fuzzy linear regression model for fuzzy input-output data based on Tanaka's approach. Then an LP-based method to derived the satisfying solution of the decision making is developed.

• 대한수학회논문집
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• 제33권3호
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• pp.973-983
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• 2018

Fuzzy linear regression model has been widely studied with many successful applications but there have been only a few studies on the fuzzy regression model with monotonic response function as a generalization of the linear response function. In this paper, we propose the fuzzy regression model with the monotonic response function and the algorithm to construct the proposed model by using ${\alpha}-level$ set of fuzzy number and the resolution identity theorem. To estimate parameters of the proposed model, the least squares (LS) method and the least absolute deviation (LAD) method have been used in this paper. In addition, to evaluate the performance of the proposed model, two performance measures of goodness of fit are introduced. The numerical examples indicate that the fuzzy regression model with the monotonic response function is preferable to the fuzzy linear regression model when the fuzzy data represent the non-linear pattern.

• 응용통계연구
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• 제10권2호
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• pp.403-411
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• 1997

본 연구에서는 시스템을 지배하는 변수들에 대한 자료가 부정확하거나 애매모호한 경우에 통계적 회귀모형의 대안으로서 제안된 퍼지 회귀모형과 그 모수 추정을 살펴본다. 그리고 사례연구를 통하여 퍼지 회귀모형의 장단점을 이해하고 결과를 비교해본다.

• 한국지능시스템학회논문지
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• 제16권4호
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• pp.499-505
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• 2006

Regularlization approach to regression can be easily found in Statistics and Information Science literature. The technique of regularlization was introduced as a way of controlling the smoothness properties of regression function. In this paper, we have presented a new method to evaluate linear and non-linear fuzzy regression model based on Tanaka's model using the idea of regularlization technique. Especially this method is a very attractive approach to model non -linear fuzzy data.

• Journal of the Korean Data and Information Science Society
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• 제12권1호
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• pp.99-101
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• 2001

In this note, we show that a linear regression model, using entropy and degree of nearness of fuzzy numbers, suggested by Wang and Li[FSS 36, 125-136] seems to be unreasonable by an example.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

• Communications for Statistical Applications and Methods
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• 제17권4호
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• pp.611-624
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• 2010

Several methods were suggested for constructing a fuzzy relationship between fuzzy independent and dependent variables. This paper reviews the use of the method by minimizing the square of the difference between an observed and a predicted fuzzy number in an ${\alpha}$-level linear regression model. We introduce a new distance between fuzzy numbers on the basis of a mode, a core point and a radius of an ${\alpha}$-level set of a fuzzy number an construct the fuzzy regression model using the proposed fuzzy distance. We also investigate sufficient condition for an equivalence in the ${\alpha}$-level regression model.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권4호
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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.