An approach to fuzzy multiple linear regression model based on the structured element theory

WANG Hua-dong, GUO Si-cong, YUE Li-zhu

Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (10) : 2628-2636.

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Systems Engineering - Theory & Practice ›› 2014, Vol. 34 ›› Issue (10) : 2628-2636. DOI: 10.12011/1000-6788(2014)10-2628

An approach to fuzzy multiple linear regression model based on the structured element theory

  • WANG Hua-dong1, GUO Si-cong1, YUE Li-zhu2
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Abstract

For multiple linear regression model which coefficients are fuzzy numbers, this paper uses least-squares approach based on fuzzy structured element theory to study analytical expression of the model. First, a new distance formula of fuzzy numbers is defined using structured element method, and also proved equivalent with one given by the paper [1] under certain conditions. But it can avoid the inconvenience of the latter caused by interval arithmetic. Fuzzy parameters are expressed by the structured element and analytical expression of fuzzy linear regression model is provided. Then we give a parameter estimation method for the model whose fuzzy parameters are LR-type fuzzy numbers. At last, an application example is presented in order to illustrate the simplification of the proposed method.

Key words

fuzzy multiple linear regression / least-squares approach / fuzzy structured element / triangular fuzzy numbers / E-distance

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WANG Hua-dong , GUO Si-cong , YUE Li-zhu. An approach to fuzzy multiple linear regression model based on the structured element theory. Systems Engineering - Theory & Practice, 2014, 34(10): 2628-2636 https://doi.org/10.12011/1000-6788(2014)10-2628

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