A group decision-making and optimization method based on relative inverse number

Group decision-making is an important branch of decision-making theory. And comprehensive ranking is an important branch of group decision-making theory. The Borda rule and Copeland rule are common ranking methods in group decision-making. This paper demonstrates that the ranked outputs of these two methods are unreasonable and cannot accurately reflect the inner structure of the ranked inputs in some cases. In order to objectively quantify the difference between two rankings, the concept of the relative inverse number (RIN) is proposed. Then a ranking rule, also called the voting rule, based on RIN is proposed. The RIN rule analyzes the structure of the ranked inputs more comprehensively than the Borda rule and the Copeland rule, and the output of the RIN rule is more precise in the sense that the alternative with more votes from the individuals is always ranked ahead in the RIN rule while may be ranked behind in other rules. However, the complexity of the RIN rule increases exponentially with the number of alternatives. Fortunately, combined with the Borda rule or other existing ranking rules, a fast solution algorithm to search the RIN rule output has been designed. In the applications of the RIN rule in science and technology evaluation, computational complexity is reduced by 105 to 1021 times utilizing the proposed algorithm.