Study And Application Of The Dependency Between The Parameter And Input Noise In Possibilistic Linear Model

Possibilistic linear model based on possibility theory has a pivotal role in fuzzy modeling and has been widely studied. When adopting possibilistic linear model, one has to adopt an appropriate free parameter h, i.e. the threshold value used to measure degree of fit. A bad choice of the threshold value will severely deteriorate the performance of the model. In most practical situations, noise often appears in real input/output data. How to determine the appropriate threshold value, especially with the existence of noise, so as to improve the noise suppressing performance of possibilistic linear model, still keeps an open problem and is a very interesting but challenging theoretical issue at the same time.In order to determine the theoretically optimal choice of the threshold value h in possibilistic linear model with the existence of noisy input, the dependencies between parameter h and the input noise in possibilistic linear model using symmetric fuzzy triangular coefficients and non-symmetric fuzzy triangular coefficients are studied. In this paper, follow the spirit of support vector regression (SVR) techniques, we first extend possibilistic linear model to its regularized version, i.e. regularized possibilistic linear model, so as to enhance its generalization capability; The regularized model is then formulated as a corresponding equivalent maximum a posteriori (MAP) framework. With the help of the MAP framework, and after a series of mathematical derivation, the approximately inversely proportional dependency relationship that the parameter h in possibilistic linear model using symmetric fuzzy triangular coefficients with the standard deviation of Gaussion noisy input, Laplacian noisy input and Uniform noisy input should follow is derived respectively. And we also prove that with the existence of typical Gaussion noisy input, the free threshold of the model using non-symmetric fuzzy triangular coefficients is inversely proportional to Gaussion noisy input. At the same time, these theoretical claims are also confirmed by the simulation results. Obviously, these important conclusions are very helpful for the practical applications of both typical possibilistic linear model and regularized possibilistic linear model.Median filter is a typical non-linear filter and is well known for removing impulsive noises. But this filter distorts the fine structure of signals as well. In order to improve the performace of median filter, based on the reaserch work of possibilistic linear model, we propose a novel adaptive filter controlled by regularized possibilistic linear models. The proposed filter achieves its effect through a weighted summation of the input signal and the output of median filter, and the weights are set based on regularized possibilistic linear models concerning the states of the input signal sequence. The large amount results of compariton experimants in this paper show that this filter can preserve image details while effectively suppressing impulsive noises. Moreover, the new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples.