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.
