6. Conclusions
Considering the fact that DMs sometimes provide their preferences which do not fully comply with reciprocity properties, this paper investigates the decision models on incomplete MPRs and FPRs without the requirement of satisfying reciprocity property. For a complete MPR A = (aij) n×n, a method to construct its corresponding consistent MPR is proposed, which preserves the original information in A = (aij) n×n as much as possible. In addition, this paper presents a new characterization of the multiplicative consistency condition, based on which a method to estimate unknown preference values in an incomplete MPR is proposed. On this basis, the final A = (aij) n×n derived by (16) is not only a consistent MPR but also has the same weight vector withA = (aij) n×n. It is worth mentioning that the methods proposed are also suitable for solving decision making problems with reciprocal MPRs and FPRs. In this situation, the method proposed derives the same results with existing methods. Furthermore,this paper mainly investigates the consistency for incomplete FPRs and MPRs not satisfying reciprocity property, thus, a corresponding study on consensus issues in GDM process needs to be carried out in future works.
