A stratified framework for handling conditional preferences: an extension of the analytic hierarchy process

Representing and reasoning over different forms of preferences is of crucial importance to many different fields, especially where numerical comparisons need to be made between critical options. Focusing on the well-known Analytical Hierarchical Process (AHP) method, we propose a two-layered framework for addressing different kinds of conditional preferences which include partial information over preferences and preferences of a lexicographic kind. The proposed formal two-layered framework, called CS-AHP, provides the means for representing and reasoning over conditional preferences. The framework can also effectively order decision outcomes based on conditional preferences in a way that is consistent with well-formed preferences. Finally, the framework provides an estimation of the potential number of violations and inconsistencies within the preferences. We provide and report extensive performance analysis for the proposed framework from three different perspectives, namely time-complexity, simulated decision making scenarios, and handling cyclic and partially defined preferences.