Post factum analysis for robust multiple criteria ranking and sorting

Abstract

Providing partial preference information for multiple criteria ranking or sorting problems results in the indetermination of the preference model. Investigating the influence of this indetermination on the suggested recommendation, we may obtain the necessary, possible and extreme results confirmed by, respectively, all, at least one, or the most and least advantageous preference model instances compatible with the input preference information. We propose a framework for answering questions regarding stability of these results. In particular, we are investigating the minimal improvement that warrants feasibility of some currently impossible outcome as well as the maximal deterioration by which some already attainable result still holds. Taking into account the setting of multiple criteria ranking and sorting problems, we consider such questions in view of pairwise preference relations, or attaining some rank, or assignment. The improvement or deterioration of the sort of an alternative is quantified with the change of its performances on particular criteria and/or its comprehensive score. The proposed framework is useful in terms of design, planning, formulating the guidelines, or defining the future performance targets. It is also important for robustness concern because it finds which parts of the recommendation are robust or sensitive with respect to the modification of the alternatives' performance values or scores. Application of the proposed approach is demonstrated on the problem of assessing environmental impact of main European cities.

Predictive analytics and disused railways requalification: Insights from a Post Factum Analysis perspective

“…The study presented in [18] aimed at supporting the local authority in the Piedmont Region in understanding what could be the most suitable requalification project for a recently abandoned railway line. The present study starts from the recommendation obtained from the above mentioned process, and focuses on the preferences of the two most important stakeholders, thus further developing the analysis through the PFA framework [36].…”

“…However, a few approaches instead focus on changes of the performances that are assigned to each action on different criteria, rather than on the parameters of the preference model (for a review, see [36]). The justification for these approaches is that such evaluations can hardly ever be viewed as deterministic entities [65].…”

“…To overcome these limitations, [36] proposed a more general framework of Post Factum Analysis (PFA), which addresses multivariate robustness and sensitivity concerns. The most important innovations proposed in this framework can be summarised as follows:…”

“…Despite large innovations proposed in PFA [36], the framework still has some limitations which negatively affect its usability. We address these drawbacks in this paper.…”

“…Finally, PFA -as originally proposed in [36] -does not allow discriminating the changes that are required/allowed on different criteria, meaning that it requires that the performances on all considered criteria are modified in the same way (e.g., that they are all improved by at least 10% or that they are deteriorated by at most 20%). By incorporating MOO into PFA, we are able to construct all possible scenarios of required or allowed modifications.…”