DISTANCE, SIMILARITY AND ENTROPY MEASURES OF N-DIMENSIONAL FUZZY SETS

An n-dimensional fuzzy set generalizes other fuzzy structures and effectively addresses real-world problems by providing greater flexibility in assigning membership values through the selection of an arbitrarily large n. Information measures are essential tools that yield significant judgments about data expressed in fuzzy form. This paper presents the concepts of n-dimensional distance measures, similarity measures, and entropy measures, accompanied by significant examples for each, and demonstrates the interrelationships among these measures. Certain specialized measures, including σ-measure, proximity measure, and linear measure, are examined, and significant results pertaining to them are derived. A succinct approximation of n-dimensional fuzzy sets is shown through the distance measure and the notion of orderless n-dimensional fuzzy sets, which proves advantageous in addressing practical issues. Ultimately, two decision-making dilemmas are resolved utilizing the concepts presented.