Incomplete Judgments in AHP: Transition-Based Approaches, Aggregation Strategies, and Their Impact on Decision Outcomes

This paper examines decision-making challenges that arise when information is incomplete, specifically when judgments are missing or unavailable in the context of individual and group applications of the Analytic Hierarchy Process (AHP). Two illustrative examples are provided. The first, adapted from a recently published study in the field of artificial intelligence, demonstrates how different methods for generating missing judgments can affect the outcomes of an individual decision-maker. The second example addresses a real-world problem of allocating farmland among three crops, wheat, corn, and soybeans, using four evaluation criteria: expenses, labor, reliability, and market considerations. In this example, two decision-makers form a group, and their incomplete judgments leave gaps in pairwise comparison matrices at different levels of the hierarchy. The solution incorporates both transition-based approaches (general transition rule and First-Level Transition Rule) and established methods such as Harker’s and van Uden’s. In addition, aggregation of individual judgments (AIJ) is applied where at least one judgment exists, while geometric aggregation is used when multiple judgments are available. This enables prioritization of decision elements in both examples, with particular attention to cases requiring a priori and a posteriori aggregation of individual judgments across hierarchical levels. A critical analysis of the results highlights key differences between methods, revealing ongoing controversies regarding their reliability in practice. Although it is shown that the First-Level Transition Rule method in the presented examples and other authors’ tests outperforms other methods used, the findings suggest that further research is needed to refine and establish more trustworthy procedures for handling incomplete information in AHP applications.