Building a type-2 fuzzy regression model based on credibility theory and its application on arbitrage pricing theory

Real life circumstances used to provide us with linguistically vague expression of data in nature. Thus, type-1 fuzzy set (T1F set) was introduced to model this uncertainty. Additionally, same words will mean variously to different people, which means ambiguous uncertainty also exists when associated with the membership function of a T1F set. Type-2 fuzzy set(T2F set) is then invented to express the hybrid uncertainty of both primary fuzziness and secondary one of membership functions. On the one hand, T2F variable models the vagueness of information better. On the other hand, those variables are hard to deal with its three-dimensional feature given. To address problems in presence of such variables with hybrid fuzziness, a new class of T2F regression model is built based on credibility theory, called the T2F expected value regression model. The new model will be developed in this paper. This paper is a further work based on our former research of T2F qualitative regression model.