Woo-Joo Lee

The statistical inferences of fuzzy regression based on bootstrap techniques

In this paper, we estimate the parameters of fuzzy regression models and investigate a statistical inferences with crisp inputs and fuzzy outputs for each

Likelihood inference based on fuzzy data in regression model

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An application of F-transform to a regression model based on Theil's method

α-cut. The proposed approaches of statistical inferences are fuzzy least squares (FLS) method and bootstrap technique. FLS is constructed on the basis of minimizing the sum of square of the total difference between observed and estimated outputs. Numerical examples are illustrated to perform the hypotheses test and to provide the percentile confidence regions by proposed approach.

Optimal properties of a fuzzy least estimator based on new operations

A new modified Fuzzy transform (F-transform) method which is combined with the bootstrap technique for forecasting is proposed in this paper. We apply the bootstrap technique to improve the accuracy of the F-transform method. An example is given to show the superior of proposed method.

A Novel Forecasting Method Based on F-Transform and Fuzzy Time Series

In regression analysis, such as other statistical inference problems, imprecise data may be encountered. In this paper, we focused on some statistical inferences in fuzzy regression model on the basis of information the supplied by the available fuzzy data based on imprecise data. For these, we consider the maximum likelihood estimates of linear regression parameters based on fuzzy data for the variety of membership functions. Numerical example is given for estimating the regression parameters in order to provide an illustration of the proposed maximum likelihood estimation.

A hybrid dynamic and fuzzy time series model for mid-term power load forecasting

Re-auction happens when a bid winner defaults on the payment without making second in-line purchase declaration even after determining sales permission. This is a process of selling under the court’s authority. Re-auctioning contract price of real estate is largely influenced by the real estate business, real estate value, and the number of bidders. This paper is designed to establish a statistical model that deals with the number of bidders participating especially in apartment re-auctioning. For these, diverse factors are taken into consideration, including ratio of minimum sales value from the point of selling to re-auctioning, number of bidders at the time of selling, investment value of the real estate, and so forth. As an attempt to consider ambiguous and vague factors, this paper presents a comparatively vague concept of real estate and bidders as trapezoid fuzzy number. Two different methods based on the least squares estimation are applied to fuzzy regression model in this paper. The first method is the estimating method applying substitution after obtaining the estimators of regression coefficients, and the other method is to estimate directly from the estimating procedure without substitution. These methods are provided in application for re-auction data, and appropriate performance measure is also provided to compare the accuracies.

Fuzzy Theil regression Model

Regression Analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variables and response variables. This paper propose a new regression analysis applying Theils method based on F-transform. The main advantage of Theils method in regression is the robustness, which means that it is not sensitive to outliers. The proposed method uses the median of rates of increments which are obtained from F-transform, based all possible pairs of F-transformed data in order to estimate the coefficients of fuzzy regression model. An example is given to show that the proposed regression analysis applying Theils method based on F-transform is more robust than the least squares estimation (LSE) and even more robust than the original Theils method.

Analysis of Variance for Fuzzy Data Based on Permutation Method

This paper deals with optimal properties of fuzzy least squares estimators of the fuzzy linear regression model with fuzzy input-output data that has an error structure. Fuzzy least squares estimators with new operations for regression parameters were proposed earlier in our previous study based on a suitable metric, and shows that the estimators are fuzzy-type linear estimators. We propose expectations and variances by using the algebraic properties of the triangular fuzzy matrices, and show some optimal properties BLUE(Best Linear Unbiased Estimator) of the estimators. Simple computational example is given to confirm these properties.