• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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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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• v.8 no.2
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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.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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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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• v.17 no.2
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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.

• 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.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.869-880
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• 2001

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input-output data using shape preserving operations based on Tanaka’s approach. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using general linear program.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.185-198
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• 2016

Regression analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper propose a fuzzy regression analysis applying Theils method which is not sensitive to outliers. This 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. An example and two simulation results are given to show fuzzy Theils estimator is more robust than the fuzzy least squares estimator.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.2
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• pp.371-383
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• 1997

This paper propose a fuzzy regression method using fuzzy neural networks when a membership value is attached to each input-output pair. First, a method of linear fuzzy regression analysis is described by interpreting the reliability of each input-output pair as its membership values. Next, an architecture of fuzzy neural networks with fuzzy weights and fuzzy biases is shown. The fuzzy neural network maps a crisp input vector to a fuzzy output. A cost function is defined using the fuzzy output from the fuzzy neural network and the corresponding target output with a membership value. A learning algorithm is derived from the cost function. The derived learning algorithm trains the fuzzy neural network so that the level set of the fuzzy output includes the target output. Last, the proposed method is illustrated by computer simulations on numerical examples.