<p>The Q-rung orthopair fuzzy set (q-ROFS) represents a generalized adaptation of the fuzzy set, specifically designed to overcome the inherent limitations posed by intuitionistic fuzzy sets and Pythagorean fuzzy sets in effectively managing uncertainty and ambiguity. The characterization of q-rung orthopair fuzzy similarity measures is significant because of their enhanced discriminative power compared to measures created for fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. These similarity measures are essential in various real-life applications, including pattern recognition, decision-making, clustering, image segmentation, and information retrieval. Therefore, this article focuses on constructing similarity measures between q-rung ortho pair fuzzy sets based on q-rung orthopair fuzzy equivalences. The primary contribution of this article is threefold. First, we expand the concept of fuzzy equivalences to include q-rung ortho pair fuzzy equivalences and offer a variety of general techniques for their derivation. Secondly, we present an innovative method for developing q-rung ortho pair fuzzy similarity measures utilizing q-rung ortho pair fuzzy equivalences. Finally, we implement the proposed methods to develop similarity-based algorithms for pattern recognition and multiple attribute decision-making (MADM). We also provide several numerical examples to demonstrate the advantages of the proposed class of q-rung ortho pair fuzzy similarity measures in both pattern recognition and decision-making. The increased accuracy in numerical experiments and the computational results of case studies related to pattern recognition and multiple attribute decision-making further validate the effectiveness and credibility of the proposed methods compared to the state-of-the-art.</p>