Abstract
In this paper, we define fuzzy interval data and introduce an approximate method for Bayesian selection of independent variables in linear regression models by using Zadeh's probability concept of fuzzy events. It is important which combination of independent variables is best when we apply the regression analysis. In this paper, we call the data whose boundaries are vague the fuzzy interval data. Here, dependent variables are observed as fuzzy interval data, so we show the posterior distribution for a combination of independent variables using the conventional independent variables and fuzzy dependent variables. This distribution is useful for selection of independent variables. But, the method with direct usage of the membership functions of fuzzy interval data is insufficient from a viewpoint of calculation. However, our proposed method's treatment of the middle points of membership functions as the representative points can solve such a problem. As a result, even if we obtain fuzzy dependent variables, we can formulate an approximate selection of independent variables which is not so far different from the conventional Bayesian selection of independent variables. In realistic situations, we do not always treat ideal symmetrical membership functions. Therefore, we carry out the computer simulations under realistic situations which do not satisfy completely the condition of the symmetry of trapezoidal membership functions. Consequently, we can show the practicability of our method.
