COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS

Year 2021, Volume: 22 Issue: 4, 353 - 365, 29.12.2021

Münevvere Yıldız , Memmedağa Memmedli

https://doi.org/10.18038/estubtda.1033350

Abstract

Statistical modeling is essential to revealing the relationships between variables. These statistical models can be classified as parametric and nonparametric methods in studies using crisp values. However, most of the collected data are inherently fuzzy. In this context, the fuzzy expression of methods using precise data is a matter of curiosity for researchers. The methods with fuzzy input and output variables have been developed for a long time. The study aims to describe nonparametric local polynomial regression models in fuzzy structure to examine the results for cases where the input variable is a crisp number, and the output variable is a symmetrical triangular and trapezoidal fuzzy number. According to the results, the bandwidth parameter was smaller in models where the degree of the polynomial was taken as one and larger in the case of three. In addition, the bandwidth parameter was found to be larger in models using the Epanechnikov kernel.

Keywords

Fuzzy local polynomial regression, Symmetric triangular fuzzy number, Trapezoidal fuzzy number, Generalized cross-validation, Mean square error

COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS

Abstract

Statistical modeling is essential in revealing the relationships between variables. These models can be classified as parametric and nonparametric methods in studies using crisp values. However, most of the data collected are inherently fuzzy. In this framework, it has been a subject that has been studied from past to present that the methods derived for exact values are expressed as methods with fuzzy valued input and output variables. The study aims to describe nonparametric local polynomial regression models in fuzzy structure to examine the results for cases where an input variable is a crisp number, and the output variable is a symmetrical triangular and trapezoidal fuzzy number. According to the results, the bandwidth parameter was smaller in models where the degree of the polynomial was taken as one and larger in the case of three. In addition, the bandwidth parameter was found to be larger in models using the Epanechnikov kernel.

Keywords

fuzzy local polynomial regression, symmetric triangular fuzzy number, trapezoidal fuzzy number, generalized cross-validation, Mean square error

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