Abstract
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.
Highlights
Fuzzy set theory was introduced by Zedah in 1964
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
Summary
Fuzzy set theory was introduced by Zedah in 1964. In the field of fuzzy regression analysis, two main methods are proposed by Tanaka and Diamond. The first approach; Tanaka [1] first proposed the fuzzy linear regression model in 1982; established the first fuzzy regression analysis model. Tanaka and Watada [3] introduced possibility measure into fuzzy linear regression. Modarres and Nasrabadi [6] proposed an fuzzy linear regression analysis from the point of view risk. Kwong and Chen [7] introduced fuzzy least squares regression approach to modelling relationships in Quality function deployment. Zhang [8] proposed an fuzzy linear regression analysis model based on the centroid method. Introduced chaos optimization algorithm (COA) determines the numerical characteristics of the random variable. The fuzzy regression coefficient of different risk models can be obtained, and model are determined
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