Study on consistency and redundancy in multi-attribute decision-making problem with incomplete information

This paper considers a multi-attribute decision-making problem with incomplete information. In such problem, it is often difficult to obtain a satisfactory decision result according to the initial incomplete information provided by decision-maker (DM). So the DM may provide more new information (i.e. new constraints of parameters). If a new constraint is redundant, then it is void for improving decision. If a new constraint is incompatible with previous ones, then the whole system becomes inconsistent. Therefore, it is very important to judge the consistency and redundancy of information in MADM problem. In this presentation, we propose the linear and nonlinear programming models to check the consistency and redundancy of information and give an approach to transform system from inconsistency to consistency by deleting the incompatible constraints. At last, whole checking procedure is also put forward.