Capturing hesitation and uncertainty in decision-making (DM) problems remains a critical challenge in many real-world applications. The picture fuzzy set (P-FS) model significantly represents positive, neutral, and negative information, and interval-valued PFSs (IVP-FSs) support additional flexibility by enabling interval-based evaluations. However, these approaches may still lack the ability to effectively model multilayered uncertainty and fluctuations of expert assessments. To handle such situations, the proposed study established an innovative fuzzy approach that combines P-FSs, IVP-FSs, and a radius parameter within a unified framework. The proposed model was termed cubic circular picture fuzzy sets (CuCP-FSs). In this proposed approach, the combination of P-FSs and IVP-FSs was crucial for capturing multilayered uncertainty, and the radius parameter represents the degree of reliability or fluctuations around the P-FS information. Several fundamental set-theoretic operations were demonstrated for the proposed CuCP-FSs framework. Moreover, Bonferroni operational laws were presented, and the corresponding aggregation operators (AOs) were designed to efficiently integrate assessment information. The essential characteristics of the proposed AOs are also investigated to ensure their validity. A multi-criteria decision-making (MCDM) technique was constructed based on these developments within the environment of CuCP-FSs. The proposed technique was employed for applications in the selection of quantum computing technology, presenting the effectiveness and practicality of the proposed MCDM approach. Furthermore, a comparative analysis with several existing fuzzy approaches was examined, which reflects the robustness and reliability of the newly defined CuCP-FS model in presenting complex uncertain information.
Citation: Haitham Qawaqneh, Abdallah Shihadeh, Wael Mahmoud Mohammad Salameh, Sultan Hussain, Muhammad Zeeshan, Takaaki Fujita. A novel cubic circular picture fuzzy set framework with Bonferroni mean operators and an illustrative application to quantum computing technology selection[J]. AIMS Mathematics, 2026, 11(5): 14412-14456. doi: 10.3934/math.2026591
Capturing hesitation and uncertainty in decision-making (DM) problems remains a critical challenge in many real-world applications. The picture fuzzy set (P-FS) model significantly represents positive, neutral, and negative information, and interval-valued PFSs (IVP-FSs) support additional flexibility by enabling interval-based evaluations. However, these approaches may still lack the ability to effectively model multilayered uncertainty and fluctuations of expert assessments. To handle such situations, the proposed study established an innovative fuzzy approach that combines P-FSs, IVP-FSs, and a radius parameter within a unified framework. The proposed model was termed cubic circular picture fuzzy sets (CuCP-FSs). In this proposed approach, the combination of P-FSs and IVP-FSs was crucial for capturing multilayered uncertainty, and the radius parameter represents the degree of reliability or fluctuations around the P-FS information. Several fundamental set-theoretic operations were demonstrated for the proposed CuCP-FSs framework. Moreover, Bonferroni operational laws were presented, and the corresponding aggregation operators (AOs) were designed to efficiently integrate assessment information. The essential characteristics of the proposed AOs are also investigated to ensure their validity. A multi-criteria decision-making (MCDM) technique was constructed based on these developments within the environment of CuCP-FSs. The proposed technique was employed for applications in the selection of quantum computing technology, presenting the effectiveness and practicality of the proposed MCDM approach. Furthermore, a comparative analysis with several existing fuzzy approaches was examined, which reflects the robustness and reliability of the newly defined CuCP-FS model in presenting complex uncertain information.
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Haitham Qawaqneh, Abdallah Shihadeh, Wael Mahmoud Mohammad Salameh, Sultan Hussain, Muhammad Zeeshan, Takaaki Fujita. A novel cubic circular picture fuzzy set framework with Bonferroni mean operators and an illustrative application to quantum computing technology selection[J]. AIMS Mathematics, 2026, 11(5): 14412-14456. doi: 10.3934/math.2026591
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