Two Novel Distances for Neutrosophic Fuzzy Sets with Applications in Decision-Making and Clustering

Neutrosophic fuzzy (NF) sets provide a powerful mathematical framework for modeling uncertainty, indeterminacy, and inconsistency features that are inherent in many real-world decision-making and data analysis problems. This study introduces two novel, axiomatically validated distance measures designed to improve analysis within NF environments. Existing distance measures often struggle with high indeterminacy and lack critical axiomatic properties, leading to unreliable outcomes in decision-making and pattern recognition. We benchmark their performance against state-of-the-art alternatives using a new NF pattern recognition algorithm. To demonstrate practical utility, the measures were integrated into the NF-TOPSIS method for multi-criteria decision-making and the NF-CLUSTER algorithm for data clustering, tested on both synthetic and real-world datasets. Experimental results confirm our measures consistently outperform existing ones, producing more discernible rankings and more cohesive clusters with an improved validity index. These findings establish a robust and effective framework for quantifying dissimilarity between NF sets, significantly advancing applications under high uncertainty and indeterminacy.