Consistent Fuzzy Analytic Hierarchy Process by Considering Fuzzy Input and Output Data

The analytic hierarchy process (AHP) has been widely used in the fields of decision-making, operations research, and management. Further extension of the AHP is also proposed to deal with the fuzzy environments or group decision-making problem by using fuzzy or interval numbers. In the AHP, the consistency index (CI) or others, e.g., consistency ratio (CR), of the AHP is viewed as an index to judge the rationality and consistency of the weights of criteria. However, these indices seem to be ignored in the fuzzy/interval AHP in the past papers. That is, the result that we simply use the conventional fuzzy/interval AHP might be inconsistent. In this paper, we propose a consistent fuzzy AHP which accounts for the concept of CI and ensure the consistent result of the weights in both the fuzzy/interval environments and group decision-making.