Selecting an optimal water purification strategy presents a complex multi-criteria decision-making problem due to inherent uncertainty, imprecise information, and conflicting evaluation criteria. Traditional fuzzy set-based approaches often lack the flexibility to accurately represent such uncertainty. To address these limitations, this study proposes a novel decision-support framework based on circular q-rung orthopair fuzzy ( \(C_{r}q\) -ROF) set, which extend conventional q-rung orthopair fuzzy sets by incorporating a circular representation to model uncertainty more expressively. A key contribution of this work is the development of an improved score function that overcomes the limited discriminative capability of existing formulations. Moreover, Schweizer–Sklar operational laws are introduced within the \(C_{r}q\) -ROF environment, and their fundamental algebraic properties are rigorously examined. Two novel aggregation operators—the \(C_{r}q\) -ROF Schweizer–Sklar weighted average and geometric operators—are constructed and validated to enhance flexibility and accuracy in aggregating expert opinions. To further improve decision reliability, the well-established multi-objective optimization by ratio analysis plus full multiplicative form (MULTIMOORA) method is extended under the \(C_{r}q\) -ROF framework. This integrated model simultaneously considers evaluation scores, ranking stability, and consistency across multiple ranking strategies, addressing key limitations of prior dominance-based integration techniques. The practicality and effectiveness of the proposed approach are demonstrated through a real-world case study focused on selecting the optimal commercial water purification method, with comparative analysis against existing decision-making techniques.
