Compact Fuzzy Set: A Parameter-Free Unifying Approach for Flexible and Reliable Conflict Modeling in Group Decision Making

While the literature on fuzzy set extensions has expanded rapidly, this extension inflation has introduced significant reliability issues regarding the semantic consistency and practical validity of the proposed models. Specifically, high levels of disagreement among experts are often relabeled as indeterminacy or suppressed through mathematical normalization in current fuzzy set extensions. Widely used frameworks, such as Pythagorean, Fermatean, and Q-rung orthopair fuzzy sets, rely on arbitrary parameters (q,t) to model these scenarios. This dependence creates synthetic indeterminacy, an artifact of the model rather than the data, leading to semantic shifts where explicit conflict is misinterpreted as hesitation. Similarly, neutrosophic sets, despite allowing independence, impose a counter-intuitive ternary structure that complicates linguistic data collection and suffer from logical paradoxes at asymptotic limits. To address these fundamental flaws without adding to the inflation, this study introduces the compact fuzzy set (CFS) as a parameter-free, unifying framework. Unlike existing extensions that impose unrealistic restrictions, CFS allows membership and non-membership degrees to be assigned completely independently. It captures high-inconsistency scenarios within a mathematical compact term without requiring normalization or data transformation, thereby preventing data loss. The validity of CFS is proven through its stability at asymptotic limits where other extensions fail, and its consistency with intuitionistic fuzzy sets. A real-world CFS-TOPSIS application on reputation management strategies demonstrates that CFS yields robust rankings even under high expert disagreement, offering a transparent and reliable alternative to the parametric complexity and semantic ambiguity of current extensions.