Dual models for possibilistic regression analysis

Upper and lower regression models (dual possibilistic models) are proposed for data analysis with crisp inputs and interval or fuzzy outputs. Based on the given data, the dual possibilistic models can be derived from upper and lower directions, respectively, where the inclusion relationship between these two models holds. Thus, the inherent uncertainty existing in the given phenomenon can be approximated by the dual models. As a core part of possibilistic regression, firstly possibilistic regression for crisp inputs and interval outputs is considered where the basic dual linear models based on linear programming, dual nonlinear models based on linear programming and dual nonlinear models based on quadratic programming are systematically addressed, and similarities between dual possibilistic regression models and rough sets are analyzed in depth. Then, as a natural extension, dual possibilistic regression models for crisp inputs and fuzzy outputs are addressed.