Fuzzy Set-Based Modelling of Uncertainty in Multi-Criteria Decision Making Systems

Real-world decision-making problems are frequently characterised by imprecision, vagueness, and subjectivity that classical crisp models cannot adequately capture. This paper presents a fuzzy set-based modelling framework for multi-criteria decision-making (MCDM) under uncertainty, in which linguistic assessments of decision-makers are represented as triangular fuzzy numbers (TFNs) and aggregated through a fuzzy extension of the Technique for Order Preference by Similarity to Ideal Solution (Fuzzy TOPSIS). The proposed methodology integrates fuzzy set aggregation, fuzzy-weighted normalisation, and vertex-based distance measures to rank competing alternatives while preserving the uncertainty inherent in expert judgement throughout the computational process, rather than eliminating it at the input stage. The framework is illustrated through a supplier-selection case study involving four alternatives evaluated by three decisionmakers against four criteria (cost, quality, delivery, and service). The resulting closeness coefficients produce a complete ranking of alternatives, and a discussion of sensitivity and robustness is provided. The results demonstrate that fuzzy set-based modelling offers a transparent, mathematically tractable, and practically implementable approach for group decision-making under uncertainty, with applicability extending to supplier selection, project evaluation, risk assessment, and other domains where qualitative judgement must be converted into defensible quantitative rankings.