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The aim of this study is to explore innovative non-linear programming (NLP) models utilizing the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, tailored for resolving decision-making challenges within the framework of cubic <inline-formula> <tex-math notation="LaTeX">$p,q-$ </tex-math></inline-formula> quasirung orthopair fuzzy sets <inline-formula> <tex-math notation="LaTeX">$({\mathrm {C}_{\mathrm {(p,q)}}}\mathrm {QOFSs})$ </tex-math></inline-formula>. In prior research, data pertaining to an element has typically been gathered in the form of either interval-valued <inline-formula> <tex-math notation="LaTeX">$p,q-$ </tex-math></inline-formula> quasirung orthopair fuzzy sets <inline-formula> <tex-math notation="LaTeX">$({\mathrm {IV}_{\mathrm {(p,q)}}}\mathrm {QOFSs})$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">$p,q-$ </tex-math></inline-formula> quasi orthopair fuzzy sets (<inline-formula> <tex-math notation="LaTeX">$p,q-$ </tex-math></inline-formula> QOFSs) information. As an alternative approach, <inline-formula> <tex-math notation="LaTeX">${\mathrm {C}_{\mathrm {(p,q)}}}\mathrm {QOFSs}$ </tex-math></inline-formula> emerges as an extension of these sets, wherein information is compiled by simultaneously considering both <inline-formula> <tex-math notation="LaTeX">${\mathrm {IV}_{\mathrm {(p,q)}}}\mathrm {QOFSs}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$p,q-$ </tex-math></inline-formula> QOFSs. Driven by this motivation, we constructed the NLP models incorporating interval weights and integrating the relative closeness coefficient concept alongside weighted distance measures. Furthermore, we scrutinized some notable characteristics (RCC) of these models. Additionally, we introduce an innovative multicriteria decision-making (MCDM) technique and illustrate its application with a real-world case study related to green supplier selection. A comparative analysis is also performed to validate the effectiveness and rationality of the method.