Consistency is an important issue that causes wide public concern of decision-makers in the decision-making process. The lack of consistency in preference relations results in a vague solution. The main goal of this paper is to achieve the consistent intuitionistic multiplicative preference relation using a graphical approach. We have proposed two different characterizations of the consistency for intuitionistic multiplicative preference relation(IMPR). In the first approaches, we propose an algorithm to achieve the consistency of IMPR by using the cycles of various length in a directed graph.
The second approach proves isomorphism between the set of IMPRs and the set of asymmetric multiplicative preference relations. That result is explored to use the methodologies developed for asymmetric multiplicative preference relations to the case of IMPRs and achieve the consistency of asymmetric multiplicative preference relation using a directed graph. Sometimes the decision maker may not be able to provide the complete relation. So the above-said method is applied for an incomplete IMPR also, here consistency plays an important role. The examples are provided to illustrate both the methods in all cases.