Building a type-2 fuzzy qualitative regression model

Type-1 fuzzy regression model is constructed with type-1 fuzzy coefficients dealing with real value inputs and outputs. From the fuzzy set-theoretical point of view, uncertainty also exists when associated with qualitative data (membership degrees). This paper intends to build a qualitative regression model to measure uncertainty by applying the type-2 fuzzy set as the model's coefficients. We are thus able to quantitatively describe the relationship between qualitative object variables and qualitative values of multivariate attributes (membership degree or type-1 fuzzy set), which are given by subjective recognition and judgment. We will build a basic qualitative model first and then improve it capable of ranging inputs. We will also give a heuristic solution in the end.