Fuzzy Linear regression based on approximate Bayesian computation

Ning Wang

doi:10.1016/j.asoc.2020.106763

2020-12-01

PRE

DOI：10.1016/j.asoc.2020.106763

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摘要

En 中文

Fuzzy linear regression with crisp inputs and fuzzy output data constitutes an important modeling problem. Basic strategies used to solve this problem, i.e., the possibilistic method and the least squares method, together with their extensions, have some drawbacks. The possibilistic methods put emphasis on an inclusion property while the least squares methods focus on a central tendency property. Therefore, many researchers work on combining these two methods to obtain a better performance. In this paper, in contrast to most existing techniques which treat fuzzy linear regression as an optimization problem, we set the problem of constructing a fuzzy linear regression model in Bayesian statistics and propose a new fuzzy linear regression method based on approximate Bayesian computation (ABC). The method applies the likelihood-free inference algorithm ABC to generate independent samples of unknown model coefficients from Bayesian posterior distribution. This overcomes difficulty of defining likelihood function in fuzzy environment. By adjusting a prior distribution and a threshold of the ABC algorithm, the proposed approach can flexibly balance the inclusion property of the possibilistic methods and the central tendency property of the least squares methods. The convergence property of the proposed ABC algorithm is verified by a numerical example. Two measuring criteria, i.e., a distance metric and a degree of fitting index, which indicate the central tendency property and the inclusion property, respectively, are introduced to evaluate the quality of regression results. Three numerical examples are applied to show the performances of the proposed method. The numerical results are also compared with those obtained by some classical and recently proposed approaches. Additionally, a practical engineering application example is used to illustrate effectiveness of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.

Keyword:

Fuzzy linear regression

Bayes statistics

Approximate Bayesian computation