Fuzzy Regression Model Based on Fuzzy Distance Measure

Some existed fuzzy regression methods have some special requirements for the object of study, such as assuming the observed values as symmetric triangular fuzzy numbers or imposing a non-negative constraint of regression parameters. In this paper, we propose a left-right fuzzy regression method, which is applicable to various forms of observed values. We present a fuzzy distance and partial order between two left-right (LR) fuzzy numbers and we let the mean fuzzy distance between the observed and estimated values as the mean fuzzy error, then make the mean fuzzy error minimum to get the regression parameter. We adopt two criteria involving mean fuzzy error (comparative mean fuzzy error based on partial order) and SSE to compare the performance of our proposed method with other methods. Finally four different types of numerical examples are given to illustrate that our proposed method has feasibility and wide applicability.

Probabilistic Fuzzy Regression Approach from the Point of View Risk

Fuzzy regression analysis is an important regression analysis method to predict uncertain information in the real world. In this paper, the input data are crisp with randomness;the output data are trapezoid fuzzy number, and three different risk preferences and chaos optimization algorithm are introduced to establish fuzzy regression model. On the basis of the principle of the minimum total spread between the observed and the estimated values, risk-neutral, risk-averse, and risk-seeking fuzzy regression model are developed to obtain the parameters of fuzzy linear regression model. Chaos optimization algorithm is used to determine the digital characteristic of random variables. The mean absolute percentage error and variance of errors are adopted to compare the modeling results. A stock rating case is used to evaluate the fuzzy regression models. The comparisons with five existing methods show that our proposed method has satisfactory performance.

Fuzzy Varying Coefficient Bilinear Regression of Yield Series

We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to estimate the coefficients and test the adaptability of the proposed model by means of generalized likelihood ratio test with SSE composite index. Finally, mean square errors and mean absolutely errors are employed to evaluate and compare the fitting of fuzzy auto regression, fuzzy bilinear regression and fuzzy varying coefficient bilinear regression models, and also the forecasting of three models. Empirical analysis turns out that the proposed model has good fitting and forecasting accuracy with regard to other regression models for the capital market.

Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

Fuzzy regression provides more approaches for us to deal with imprecise or vague problems. Traditional fuzzy regression is established on triangular fuzzy numbers, which can be represented by trapezoidal numbers. The independent variables, coefficients of independent variables and dependent variable in the regression model are fuzzy numbers in different times and TW, the shape preserving operator, is the only T-norm which induces a shape preserving multiplication of LL-type of fuzzy numbers. So, in this paper, we propose a new fuzzy regression model based on LL-type of trapezoidal fuzzy numbers and TW. Firstly, we introduce the basic fuzzy set theories, the basic arithmetic propositions of the shape preserving operator and a new distance measure between trapezoidal numbers. Secondly, we investigate the specific model algorithms for FIFCFO model (fuzzy input-fuzzy coefficient-fuzzy output model) and introduce three advantages of fit criteria, Error Index, Similarity Measure and Distance Criterion. Thirdly, we use a design set and two reference sets to make a comparison between our proposed model and the reference models and determine their goodness with the above three criteria. Finally, we draw the conclusion that our proposed model is reasonable and has better prediction accuracy, but short of robust, comparing to the reference models by the three goodness of fit criteria. So, we can expand our traditional fuzzy regression model to our proposed new model.

Estimate Beta Coefficient of CAPM Based on a Fuzzy Regression with Interactive Coefficients

In the Capital Asset Pricing Model (CAPM), beta coefficient is a very important parameter to be estimated. The most commonly used estimating methods are the Ordinary Least Squares (OLS) and some Robust Regression Techniques (RRT). However, these traditional methods make strong as sumptions which are unrealistic. In addition, The OLS method is very sensitive to extreme observations, while the RRT methods try to decrease the weights of the extreme observations which may contain substantial information. In this paper, a novel fuzzy regression method is proposed, which makes less assumptions and takes good care of the extreme observations. Simulation study and real word applications show that the fuzzy regression is a competitive method.

Robust Regression Analysis with LR-Type Fuzzy Input Variables and Fuzzy Output Variable

In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed model based on the Weighted Least Squares estimation procedure. Some properties of the estimates are proved. We also define suitable goodness of fit index and its adjusted version useful to evaluate the performances of the proposed model. Based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure, we give robust estimation steps for the proposed model. Compared with the well-known fuzzy Least Squares method, the effectiveness of our model on reducing the outliers influence is shown by using two examples.

Fabrication of CuFe_(2)O_(4)/Bi_(12)O_(17)Cl_(2) photocatalyst with intrinsic p-n junction for highly efficient bisphenol A degradation

The construction and application of novel highly efficient photocatalysts have been the focus in the field of environmental pollutant removal.In this work,a novel CuFe_(2)O_(4)/Bi_(12)O_(17)Cl_(2)photocatalysts were synthesized by simple hydrothermal and chemical precipitation method.The fabricated CuFe_(2)O_(4)/Bi_(12)O_(17)Cl_(2)composite exhibited much higher photocatalytic activity than pristine CuFe_(2)O_(4)and Bi_(12)O_(17)Cl_(2)in the removal of bisphenol A(BPA)under visible-light illumination,which ascribed to the intrinsic p-n junction of CuFe_(2)O_(4)and Bi_(12)O_(17)Cl_(2).The photocatalytic degradation rate of BPA on CuFe_(2)O_(4)/Bi_(12)O_(17)Cl_(2)with an optimized CuFe_(2)O_(4)content(1.0 wt.%)reached 93.0%within 30 min.The capture experiments of active species confirmed that the hydroxyl radicals(·OH)and superoxide radicals(·O_(2)^(-))played crucial roles in photocatalytic BPA degradation process.Furthermore,the possible degradation mechanism and pathways of BPA was proposed according to the detected intermediates in photocatalytic reaction process.