Diagram Illustrations of Aggregation Operations for the Intuitionistic Fuzzy Values

Atanassov (Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986) 87–96) proposed the intuitionistic fuzzy set (A-IFS) that is a generalization of Zadeh's fuzzy set. The essential elements of an A-IFS are intuitionistic fuzzy values (IFVs), each of which is depicted by a membership degree and a non-membership degree. The existing literature only gives the explanation of the meaning and the aggregation operators of IFVs, which is very hard and non-visualized for us to comprehend. To overcome the above shortcomings, this paper puts forward the diagram method to analyze the structures of the basic aggregation operations of IFVs. In addition, this paper utilizes the diagram method which is similar to joint probability distribution to describe the components of aggregation operations of IFVs, and each IFV depicts a 3-dimensional vector which is regarded as the marginal distributions of the joint probability distribution.