Building linguistic random regression model from the perspective of type-2 fuzzy set

Information given in linguistic terms around real life sometimes is vague in meaning, as type-1 fuzzy set was introduced to modulate this uncertainty. Meanwhile, same word may result in various meaning to people, indicating the uncertainty also exist when associated with the membership function of a type-1 fuzzy set. Type-2 fuzzy set attempt to express the hybrid uncertainty of both primary and secondary fuzziness, in order to address regression problems, we built a type-2 Linguistic Random Regression Model based on credibility theory. Confidence intervals are constructed for fuzzy input and output, and the proposed regression model give a rise to a nonlinear programming problem focus on a well-trained model, which would be helpful and useful in linguistic assessment cases. Finally, a numerical example is provided.