A method based on preference degrees for handling hybrid multiple attribute decision making problems

In this paper, we investigate hybrid multiple attribute decision making problems with various forms of attribute values (real numbers, linguistic labels, interval numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers). We propose a method based on preference degrees which may take the forms of fuzzy numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers. The method first normalizes various forms of attribute values into preference degrees, and then uses a preference degree-based weighted averaging operator to aggregate the normalized preference degrees. Meanwhile, for convenience of calculation, a new linguistic representation model is presented, whose feasibility is verified by comparing it with the traditional 4-tuple linguistic representation model, and from our model, the mapping relationship between interval intuitionistic fuzzy numbers and linguistic labels can be constructed. Finally, we illustrate the rationality and practicality of the proposed method by an application example.

Research highlights
► Develop a new method based on preference degrees which may take the forms of fuzzy numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers.
► Develop a new linguistic representation model.
► Construct the mapping relationship between interval intuitionistic fuzzy numbers and linguistic labels.