Analyzing Uncertainty and Hesitation in Refereeing Decision using Neutrosophic Vague N-Soft Sets: A Case Study of Officiating Ability Evaluation for National-Level Volleyball Referees

Officiating in volleyball and similar high-stakes sports involves speedy, high-pressure decision-making, which is usually influenced by uncertainty, hesitation, and subjective interpretation. This study proposes a novel Neutrosophic Vague N-Soft Sets (NVNSS) framework for the evaluation of national-level volleyball referees to model as well as analyze the inherent vagueness and indeterminacy in decisions. Our framework integrated expert linguistic evaluations across multiple criteria into a structured NVNSS decision matrix. Then, we propose a risk-aware degree of support to quantify each referee’s performance under uncertainty, followed by a discrete rating assignment. Our framework introduces a robust and flexible NVSNSS scoring function that accounts for weighted contributions, non-linear transformations, and uncertainty handling to generate a well-distributed and expressive crisp value. By pairing the scores and rates of NVSNSS in the decision space, we can derive referee rankings under each criterion. Then, we propose a novel weighted aggregation that integrates entropy-based weighting to deliver the final ranking from the Assuming criteria-based rankings without being affected by large deviations across criteria. Proof-of-concept analyses are provided to validate the applicability of our framework on a real-world case study for volleyball officiating, and the results demonstrated that work is a pioneering approach for modeling uncertainty and hesitation in refereeing decisions.