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

Abstract

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. 

DOI: 10.5281/zenodo.15127379