An innovative distance measure for quantifying the dissimilarity between Q-Rung orthopair fuzzy sets

Q-Rung orthopair fuzzy set (Q-ROFSs) is a generation of quartic fuzzy sets (QFSs), Fermatean fuzzy sets (FFSs), Pythagorean fuzzy sets (PFSs), Intuitionistic fuzzy sets (IFSs), and fuzzy sets (FSs). Fuzzy similarity measures find wide-ranging applications in several fields, such as pattern recognition (PR), classification, and multi-criteria decision-making (MCDM). The computation of criteria weights in MCDM heavily relies on the fuzzy environment. Therefore, this study focuses on developing a similarity measure for Q-ROFS based on Hausdorff distance, a valuable tool for establishing object similarities. We introduce an innovative distance measure designed to quantify the dissimilarity between Q-ROFSs. Our approach leverages this distance measure to establish a similarity measure between Q-ROFSs. Furthermore, we present a set of properties associated with the suggested similarity measures. To demonstrate the usefulness of these measures, we provide numerous numerical examples in the fields of PR and linguistic variable characterization. By leveraging our innovative techniques, we also develop a novel algorithm for orthopair fuzzy Tomada de Decisao Iterativa Multicriterio (TODIM), a highly interactive and effective MCDM approach. Moreover, we have successfully applied the newly devised orthopair fuzzy TODIM method to address MCDM challenges encountered in diverse real-life problems. The obtained algebraic outcomes affirm that the suggested similarity measures are appropriate, practical, and applicable for queries involving fuzzy linguistic variables in MCDM contexts.