Research On The Improvement Of Fuzzy Varying Coefficient Regression Model With Its Applications

Fuzzy regression analysis, which is a perfect combination of fuzzy theory andclassical regression analysis, has attracted many scholars since the fuzzy regressionmodel was first established by Tanaka et al in1982. Fuzzy regress theory and itsapplications have been developed rapidly during a few decades.As one of fuzzy regression models, the fuzzy varying coefficient regression modelconsiders both the fuzziness and the nonlinearity of regression function. Thus this modelhas certain advantages in dealing with time series data under fuzzy environment.Research on the fuzzy varying coefficient regression has the important significance forthe theory and applications of fuzzy regression model. Therefore, it is an importantresearch direction.First of all, this thesis summarized the development and status of fuzzy regressmodel, especially introduced the fuzzy varying coefficient model. The concept of fuzzynumber and fuzzy number distance, related regression models were also presented in thethesis.Secondly, considering the fuzzy number is the Gaussian fuzzy number, this thesispresented fuzzy varying coefficient regress model based RWLS, and fuzzy varyingcoefficient regress model with the missing partial data. Then generalized this method tothe financial field, and this method used in fund evaluation was studied.Thirdly, a fuzzy varying coefficient regression model with fuzzy-input andfuzzy-output was discussed, and the method of corresponding parameter estimation wasproposed, that is fuzzy varying coefficient regress with new fuzzy operations. An actual example was given to compare fuzzy varying coefficient regress model with fuzzy linearregress model.Finally, a fuzzy varying coefficient regression estimation method based on varyingcoefficient regression model was proposed. By using cut set, the fuzzy varyingcoefficient regression model was transformed into the classical varying coefficientregression model to get the final data. Two practical examples were used to verify thepracticability of the presented method.