Study on Consistency and Redundancy of Incomplete Information

The consistency and redundancy of information is studied in this article. In a multi-attribute decision-making problem with incomplete information about weights, it is often difficult to obtain a satisfactory decision result based on the initial information provided by the decision-maker (DM). Therefore the DM may provide more new information, which may be compatible, incompatible, or redundant with the previous one. In this article, several mathematical programming models are proposed for checking the consistency and redundancy of information. Then, an approach that transforms parameter system from inconsistency to consistency by deleting the incompatible constraints is given. Finally, an example is presented for illustrating the validity and feasibility of the models and the approach proposed in this article.