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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation> 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.

A Quasirung Orthopair Fuzzy Hamy Mean-Based Decision Support Framework with Application to E-Learning Platform Selection

期刊论文
出版模式：

开放获取
发表日期：

2026年2月2日

查看全文

Muhammad Rahim,
Shah Zeb Khan,
Muhammad I. Syam,
Sanaa Ahmed Bajri,
Sultan S. Alodhaibi,
Hamiden Abd El-Wahed Khalifa

摘要

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 \(p\) 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.