Comparative Study on Mathematical Foundations of Type-2 Fuzzy Set, Rough Set and Cloud Model
Mathematical representation of a concept with uncertainty is one of foundations of Artificial Intelligence. The type-2 fuzzy set introduced by Mendel studies fuzziness of the membership grade of a concept. Rough set proposed by Pawlak defines an uncertain concept through two crisp sets. Cloud model, based on probability measure space, automatically produces random membership grades of a concept through a cloud generator. The three methods all concentrate on the essentials of uncertainty and have been applied in many fields for more than ten years. However, their mathematical foundations are quite different. The detailed comparative study on the three methods will discover the relationship in the betweens, and provide a fundamental contribution to Artificial Intelligence with uncertainty.