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Green supplier selection is a critical multi-criteria decision making (MCDM) problem in green supply chain management, requiring evaluation of multiple suppliers under economic, environmental, and social criteria while handling vague, imprecise, and conflicting expert judgments. Existing fuzzy-based MCDM approaches often have limitations in representing uncertainty flexibly, as they rely on fixed boundaries for membership and non-membership degrees, which may constrain decision-makers expressive capability and reduce robustness in complex environments. To address these challenges, this study proposes a novel MCDM framework based on circular p,q-quasirung orthopair fuzzy sets (C pq QOFSs), which extend p,q-quasirung orthopair and circular q-rung orthopair fuzzy sets by introducing circular regions with adjustable centers and radii. This enables more flexible and realistic modeling of uncertainty. We develop fundamental set-theoretic operations, score and accuracy functions, distance measures, and Sugeno–Weber weighted aggregation operators for C pq QOFSs, which are then employed to construct the proposed multi-criteria group decision-making (MCGDM) framework. The framework is applied to a green supplier selection problem evaluated by five focus groups, led by a panel of five field experts with extensive knowledge and experience in environmental sciences, supply chain management, logistics, procurement, sustainability, and social welfare, using four critical sustainability-related criteria. The results yield a clear ranking of alternatives that can well identify the most suitable supplier. Sensitivity analysis further validates the robustness of the ranking. In addition, a comparative analysis with existing fuzzy sets and their various extensions demonstrates the superiority and effectiveness of the proposed approach. Compared to more complex extensions such as neutrosophic sets, the C pq QOFS-based framework provides sufficient flexibility and expressive power while maintaining mathematical tractability and ease of implementation. The results confirm that the proposed approach is a robust and practical tool for solving complex MCDM problems under uncertainty.

This study proposes novel operational laws that extend the Frank t-norm and t-conorm to develop a new class of aggregation operators (AOs), namely the quasirung orthopair fuzzy Frank weighted average, weighted geometric, ordered weighted average, and ordered weighted geometric operators. These operators are specifically designed to manage uncertain and imprecise information within multi-attribute group decision-making (MGADM) environments. The proposed operators exhibit desirable mathematical properties such as flexibility, robustness, and compatibility, making them highly suitable for complex fuzzy decision contexts. Flexibility is notably enhanced through the independent tuning of the parameters , , and , allowing for more refined control over membership (MD), non-membership (NMD), and interaction behaviors. An entropy-based approach is employed to objectively determine unknown attribute weights, minimizing subjective bias. A real-world case study on the selection of an optimal investment location demonstrates the practical applicability of the proposed method. The results show an improvement in decision-making accuracy by approximately 7.5% compared to traditional approaches. Sensitivity analysis confirms the stability and reliability of the proposed operators under varying conditions. Comparative results further highlight the method’s superiority in terms of accuracy, interpretability, and adaptability to input variations. The paper concludes by outlining special cases and acknowledging certain limitations, offering directions for future research.

Selecting sustainable suppliers in the new energy vehicle industry is a complex decision-making problem due to diverse criteria, uncertainty in evaluations, and the need to prioritize certain factors. Addressing this gap, we propose a novel multi-criteria decision-making (MCDM) framework based on p ,  q -quasirung orthopair fuzzy ( ROF) sets and enhanced with Aczel–Alsina–based prioritized aggregation operators. Specifically, we develop two base operators—the ROF AA prioritized average ( ROFAAPA) and the ROF AA prioritized geometric ( ROFAAPG)—along with their weighted prioritized counterparts, the ROF AA prioritized weighted average ( ROFAAPWA) and the ROF AA prioritized weighted geometric ( ROFAAPWG). The mathematical properties of these operators are established, and an MCDM algorithm is formulated to incorporate decision-makers’ priority structures. The framework also integrates a mathematical formulation to objectively determine criteria weights, ensuring a balanced combination of subjective and data-driven inputs. A case study for a leading new energy vehicle manufacturer demonstrates the framework’s effectiveness: among four evaluation criteria—Quality ( ), Cost ( ), Service level ( ), and Production capacity ( )—Cost ( ) received the highest weight (0.2789), and supplier emerged as the most sustainable choice. Comparative experiments against established MCDM techniques confirm the proposed approach’s superior ranking stability and robustness. These results provide both a methodological advance for fuzzy decision-making research and a practical decision-support tool for industries pursuing environmentally responsible supply chain strategies.

Linguistic term fuzzy sets provide an intuitive way to express preferences, enhancing understanding and communication among decision-makers. In this article, we introduce the novel concept of p , q- quasirung orthopair fuzzy linguistic sets ( p , q- QOFLSs), which merge the principles of p , q- quasirung orthopair fuzzy sets ( p , q- QOFSs) with linguistic fuzzy sets. This new framework offers a more robust approach to handle uncertain and imprecise information in decision-making processes, characterized by linguistic membership and non-membership degrees. We establish several fundamental operational laws, alongside score and accuracy functions, to facilitate the comparison of p , q- quasirung orthopair fuzzy linguistic numbers. Leveraging these operational laws, we propose a series of weighted averaging and geometric operators under p , q- QOFLSs. Furthermore, we formulate a multi-attribute decision-making methodology using these operators. The significance of the proposed method lies in its ability to model complex decision-making scenarios with enhanced precision. A numerical example validates the practicality and adaptability of the methodology, supported by sensitivity analyses and comparative evaluations, highlighting the innovation and efficiency of the approach.

The Bonferroni mean (BM) operator provides a strategy for justifying the effects of unrealistic aggregation values while simultaneously capturing the interconnections between input arguments. Moreover, p , q -quasirung orthopair fuzzy ( p , q - -QOF) sets is a new development in fuzzy set (FS) theory that allows for more accurate and nuanced management and representation of uncertain data. In this paper, we integrate the concept of p , q -QOF numbers ( p , q -QOFNs) and extend the BM operators to accommodate p , q -QOF information. To aggregate diverse preferences of decision-makers, we first present some Bonferroni mean and weighted Bonferroni mean averaging operators for p , q -QOFNs. Subsequently, we construct a decision-making (DM) framework utilizing the proposed operators within the context of p , q -QOF sittings, demonstrated through a numerical illustration. Finally, we compare the presented approach with existing methods to establish the practicality and feasibility of the proposed DM process.

In this paper, we propose a novel multi-attribute group decision making (MAGDM) approach under the p ,  q -quasirung orthopair fuzzy number ( p ,  q -QOFN) environment. For this, we propose new multiplication operation and scalar power operation for p ,  q -QOFNs based on Yager’s norm. Then, by using the proposed multiplication operation and scalar power operation of p ,  q -QOFNs and the concept of prioritized geometric aggregation operator (AO), we propose the p ,  q -quasirung orthopair fuzzy Yager prioritized weighted geometric ( p ,  q -QOFYPWG) AO for aggregating p ,  q -QOFNs. We also prove the different properties of the proposed p ,  q -QOFYPWG AO of p ,  q -QOFNs. However, based on the proposed p ,  q -QOFYPWG AO, we propose a new MAGDM approach in the context of p ,  q -QOFNs environment. Afterwards, we utilize the proposed MAGDM approach to solve the different MAGDM problems, and compare the preference orders (POs) obtained from the proposed MAGDM approach to POs obtained from other existing MAGDM approaches. The proposed MAGDM approach can overcome the shortcomings of the existing MAGDM approaches, where they cannot distinguish the POs of the alternatives in some cases. The proposed MAGDM approach provides a very useful approach to deal with MAGDM problems in the p ,  q -QOFNs environment.

The Hamy mean (HM) operator is a powerful parameterized aggregation tool that enables flexible modeling of both conjunctive and disjunctive decision-making behaviors within a unified mathematical framework. Its tunable nature makes it more versatile than traditional fixed aggregation operators such as the arithmetic mean, maximum, or minimum, which are often too rigid to capture the nuanced interactions among decision criteria. Despite its proven potential in other fuzzy environments, the HM operator has not yet been developed in the context of p , q  − quasirung orthopair fuzzy ( p , q  − QOF) sets, a generalized and more expressive extension of orthopair fuzzy models that can handle higher degrees of uncertainty, vagueness, and hesitation. To address this gap, we introduce some novel aggregation operators: the p , q  − QOF interaction weighted Hamy mean ( p , q  − QOFIWHM) and the p , q  − QOF interaction weighted dual Hamy mean ( p , q  − QOFIWDHM) operators. The proposed operators inherit the parametric adaptability of the HM while incorporating the enhanced representational capabilities of p , q  − QOF sets. This combination offers significant flexibility in capturing interrelationships among criteria, making the operators well-suited for complex, large-scale, and time-sensitive decision problems. Based on these operators, we develop a multicriteria group decision-making (MCGDM) framework capable of effectively managing heterogeneous expert opinions, uncertain information, and high-dimensional evaluation data. The applicability and effectiveness of the proposed approach are demonstrated through a comprehensive case study on an E-Learning Platform selection. In this study, assessments from three domain experts were considered for 20 candidate platforms evaluated against 20 criteria encompassing technical, pedagogical, usability, and security aspects, such as system performance, course management capabilities, adaptability of learning content, cost-effectiveness, user interface quality, scalability, and data security. A detailed sensitivity analysis of parameters and q, as well as of criteria weights, was conducted to examine the robustness of the model. Furthermore, extensive stability and accuracy tests revealed that the proposed approach consistently outperformed existing aggregation operator-based methods, achieving superior accuracy (93.13%), stability (98.83%), and computational efficiency. Comparative analysis confirmed that the p , q  − QOFIWHM and p , q  − QOFIWDHM-based MCGDM framework not only improves decision reliability but also provides a scalable and adaptable tool for real-world decision-making scenarios.