Study on undecided multi-criteria decision-making based on compatibility relations theory models

The ranking of interval numbers is an important research topic for undecided multiple-criteria decision-making (MCDM) problems. This paper mainly focuses on the problem that different interval numbers have the same possibility degree values in MCDM with interval numbers. First, we propose three compatibility relations theory models corresponding to different risk preferences type decision-makers to determine the advantage relation for interval numbers. Second, we propose the advantage relation and advantage degree of the alternatives and advantage matrix to rank all the alternatives as well as select the best one based on the advantage values of alternatives. Finally, we use a realistic example to demonstrate the feasibility and effectiveness of this new ranking technology.