Linear Regression Analysis by Possibilistic Models

Abstract

Fuzziness must be considered in systems where human estimation is influential. Since Zadeh has introduced the concept of possibility, fuzziness of system equations has been grasped by possibility distributions. Possibilistic linear systems have been studied as fuzzy arithmetic operations of fuzzy numbers by the extension principle. In this paper, possibilistic linear systems are applied to the linear regression analysis which is called possibilistic linear regression. In the background of usual regression models, deviations values are supposed to be due to observation errors. Here, on the contrary, it is assumed that these deviations depend on the possibility of parameters in systems structure. More specifically, linear systems with parameters of fuzzy numbers are considered as possibilistic linear models. The estimated values obtained from the possibilistic linear model are fuzzy numbers which represent the possibility of the system structure, while the conventional confidence interval is related to the observation errors. This possibilistic linear regression analysis might be useful for finding a fuzzy structure in a fuzzy environment.