Fuzzy analytic network process and its application to the development of decision support systems

In this paper we propose a fuzzy extension of the analytic network process (ANP) that uses uncertain human preferences as input information in the decision-making process. Instead of the classical Eigenvector prioritization method, employed in the prioritization stage of the ANP, a new fuzzy preference programming method, which obtains crisp priorities from inconsistent interval and fuzzy judgments is applied. The resulting fuzzy ANP enhances the potential of the ANP for dealing with imprecise and uncertain human comparison judgments. It allows for multiple representations of uncertain human preferences, as crisp, interval, and fuzzy judgments and can find a solution from incomplete sets of pairwise comparisons. An important feature of the proposed method is that it measures the inconsistency of the uncertain human preferences by an appropriate consistency index. A prototype decision support system realizing the proposed method is developed, and its performance is illustrated by examples.