Abstract: The probability reasoning method, fuzzy reasoning method, evidential reasoning method and other reasoning methods are main techniques employed in intelligent systems for processing uncertain and vague information. The concept of inclusion degree was proposed earlier and it has been proved that the methods mentioned above are examples of inclusion degrees. In this paper, we introduce type S1 and type S2 inclusion degrees, discuss the relationship between them, and further propose inclusion degrees on interval numbers, divisions, vectors and set vectors. This paper addresses an uncertainty analysis method with different inclusion degrees for intelligent systems and other systems such as fuzzy relational databases.