Regression model based on fuzzy random variables

Classical model of regression analysis is an effective statistical one to deal with statistical data. In the past two decades, to cope with fuzzy environment where human subjective estimation is influential in regression models, various fuzzy regression models are presented for fuzzy input-output data through the theory of fuzzy sets and possibility. For instance, Tanaka et al. [22] presented linear regression analysis to cope with fuzzy data in stead of statistical data. Tanaka and Watada [25] [26] [29] presented possibilistic regression analysis based on the concept of possibility in stead of fuzziness. Watada et al. built fuzzy time-series model using intersection of fuzzy numbers [32] [34]. Also Watada tried to solve fuzzy regression model for fuzzy data [33] but it should employ heuristic methods to solve production between fuzzy numbers. Watada and Mizunuma [35] and Yabuuchi and Watada [28] built switching fuzzy regression model to analyze mixed data obtained from plural systems. Linguistic regression model is proposed by Toyoura and Watada [27]. On the other hand, the concept of fuzzy statistics plays a central role in building a fuzzy regression model [30] as well as the concept of fuzzy numbers.