Ranking of Fuzzy Numbers and their Extension via Measures with Applications

Abstract

This study introduces advanced ranking techniques for extended fuzzy numbers, specifically in both an intuitionistic fuzzy environment and a neutrosophic environment. In the intuitionistic fuzzy setting, a novel ranking method is proposed using a similarity measure based on intuitionistic fuzzy bi-implicators. This approach is applied to rank extended fuzzy numbers and is further employed in the context of multicriteria decision-making problems. Additionally, in the neutrosophic environment, the work presents an artificial intelligence-based ranking methodology for extended fuzzy numbers (neutrosophic environment), utilizing cardinality-based similarity measures. This method involved the development of structures for Jaccard, Dice, and Sokal-Sneath-2 similarity measures. The research demonstrates the consistent ranking results across these measures for Single-Valued Neutrosophic Numbers (SVNNs), emphasizing the broad applicability of the proposed approach. The method's flexibility is highlighted by the incorporation of three distinct human mind states (optimistic, pessimistic, and neutral) through logical operators.