Inconsistency reduction in decision making via multi-objective optimisation

Abstract

Within Multi-Criteria Decision Analysis (MCDA), pairwise comparison facilitates a separation of concerns helping to accurately represent a decision maker's preferences. Inconsistency within a set of pairwise comparisons has adverse effects upon the accuracy of the preferences derived from them. Inconsistency within pairwise comparisons is almost inevitable, hence consideration of its reduction is essential. This paper presents INSITE, an approach to inconsistency reduction within a set of pairwise comparisons via multi-objective optimisation. When seeking to reduce inconsistency within a set of pairwise comparisons there is a trade-off between alteration to the comparisons and the reduction of inconsistency within them. For such trade-offs no trade-off solution is superior per se to the others. Therefore, INSITE seeks to optimally reduce inconsistency within a set of comparisons by modelling inconsistency and alteration as separate objectives. In this way the nature of the trade-offs between inconsistency reduction and alteration are revealed, thus better informing a decision maker's awareness and knowledge of the problem and increasing validity of outcomes by providing a more evidential, transparent, auditable and traceable process. In this way a decision maker can look to make a more informed choice of the level of trade-off that is most suitable for them. INSITE is flexible regarding how inconsistency within judgments is measured; alteration to a decision maker's views is modelled via fine-grained measures of compromise that seek to be meaningful and relevant. Furthermore, the approach allows a decision maker to set constraints on both inconsistency and measures of compromise objectives.