A new consistency concept for interval multiplicative preference relations

Display Omitted A new consistency concept for IMPRs is defined.It is a natural extension of Saatys consistency concept for crisp case.It is robust to the permutation of the object labels.Models to address inconsistent and incomplete IMPRs are built.An algorithm to IMPRs is presented. Consistency analysis is very important to ensure the reasonable ranking order. However, all previous consistency concepts for interval multiplicative preference relations (IMPRs) are insufficient to address this type of preference relations. This paper introduces a new consistency concept for IMPRs that is a natural extension of the Saatys consistency concept for multiplicative preference relations. Several desirable properties are discussed, and the relationship between the new concept and two previous ones is studied. Then, a method to judge the consistency of IMPRs is proposed. Considering the inconsistent case, a 01 mixed programming model to derive consistent IMPRs from inconsistent ones is established. To determine missing values in incomplete HFPRs, 01 mixed programming models are constructed that can address the situation where ignore objects exist. Meanwhile, illustrative examples are offered to show the feasibility and efficiency of the developed theoretical results, and comparison analysis is provided. Finally, a consistency analysis based algorithm to decision making with IMPRs is developed that can address inconsistent and incomplete cases.

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