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

Abstract

Type‐2 (T2) fuzzy set was introduced to model vagueness associated with primary membership function of type‐1 (T1) fuzzy set. While it was invented to handle more fuzzy information, there are only a few algorithms (models) to deal with data in the form of T2 fuzzy variables given their three‐dimensional features. To solve the problem, we define the expected value of a T2 fuzzy variable using credibility theory in this paper. And by substituting the expected value for the original T2 fuzzy set, the vertical uncertainties of data are transferred to horizontal ones without much distortion of information. Calculations between three‐dimensional T2 fuzzy sets are thus transferred to two‐dimensional range calculations between T1 fuzzy sets. Based on that principle, we also build a T2 fuzzy expected regression model and apply it to the arbitrage pricing theory. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.