A Novel Multi-Criteria Decision-Making Methodology: The Presence–Absence Synthesis Method

Traditional multi-criteria decision-making methods often operate on the assumption of symmetry, presupposing that the positive impact of a criterion’s presence is perfectly complementary to the negative impact of its absence. However, in real-world decision problems, this relationship is frequently asymmetric; some criteria act merely as “delighters,” while others represent “must-have” constraints. This study proposes a novel methodology, the Presence–Absence Synthesis (PAS) Method, which addresses this asymmetry by treating the “Presence Effect” and “Absence Effect” of criteria as two independent dimensions. The method is built upon intuitionistic fuzzy sets (IFSs) to effectively model the uncertainty and hesitation inherent in expert evaluations. The applicability of the proposed approach is demonstrated through a real-world workforce management problem aimed at assigning employees to the most suitable tasks based on their competencies in a retail store. In the study, the suitability scores derived from the PAS method are integrated into a mathematical optimization model for weekly employee scheduling, presenting a two-stage decision support framework. The results and comparisons with the Technique for Order Preference by Similarity to Ideal Solution method reveal that the PAS method more effectively distinguishes critical competency gaps (i.e., criteria with high absence effects), leading to more realistic task assignments and a measurable reduction in operational risks, such as skill mismatches and infeasible schedules. Furthermore, sensitivity analysis confirms that the proposed model yields consistent and robust results under varying conditions. Beyond the retail context, the proposed PAS framework is applicable to a wide range of decision-making problems, including healthcare staff allocation, project team formation, supplier selection, and other resource allocation settings where their presence cannot compensate for the absence of critical criteria.