Research Article
Control and Optimization
Ali Dehghani Filabadi; Hossein Nahid Titkanlue
Abstract
Addressing complex decision-making scenarios, particularly those involving multiple criteria and expert perspectives, often requires robust frameworks capable of managing uncertainty and qualitative assessments. The Qualitative Absolute Order-of-Magnitude (QAOM) model offers ...
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Addressing complex decision-making scenarios, particularly those involving multiple criteria and expert perspectives, often requires robust frameworks capable of managing uncertainty and qualitative assessments. The Qualitative Absolute Order-of-Magnitude (QAOM) model offers a flexible approach for expressing subjective evaluations through linguistic terms with adjustable levels of detail. However, practical challenges remain in applying QAOM, including the absence of an inherent system for deriving attribute weights, limitations in coherently synthesizing the judgments from multiple experts, and the lack of systematic normalization procedures for negatively oriented attributes. To address these issues, this paper proposes an advanced multi-attribute group decision-making (MAGDM) framework fully embedded within the QAOM paradigm. The proposed solution introduces a mathematically consistent metric for comparing linguistic assessments, an entropy-based attribute weighting approach rooted in qualitative information, and an aggregation process that reflects expert diversity. Furthermore, a specialized normalization protocol is developed to handle negative attributes across heterogeneous scales. The feasibility and advantages of the method are validated through comprehensive examples and comparative analyses, highlighting improvements over traditional techniques in terms of objectivity, flexibility, and analytical depth. Overall, these developments markedly enhance the capabilities of QAOM-based MAGDM, equipping decision-makers with more nuanced and reliable tools for tackling complex problems characterized by imprecision and divergent expert opinions.
Research Article
Control and Optimization
Mohammad Alsaeedi; Mostafa Tavakolli; Ahmad Abouyee; Khatere Ghorbani Moghadam; Reza Ghanbari
Abstract
In this study, we proposed a novel graph partitioning problem where the edges are characterized by trapezoidal fuzzy numbers. A linear ranking function is employed to establish an order among these fuzzy numbers. We derive the necessary conditions for the existence of an ...
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In this study, we proposed a novel graph partitioning problem where the edges are characterized by trapezoidal fuzzy numbers. A linear ranking function is employed to establish an order among these fuzzy numbers. We derive the necessary conditions for the existence of an optimal solution to this problem. To address the fuzzy graph partitioning problem, we implement and compare the performance of three algorithms: Genetic Algorithm, Tabu Search, and Sequential Least Squares Programming. The algorithms are evaluated based on objective values, computational time, and the number of iterations across multiple numerical examples. Utilizing Dolan-Moré performance profiles, we demonstrate the superiority of our proposed approach relative to existing methods. The findings highlight the robustness and computational efficiency of our methodology, making a meaningful contribution to the advancement of fuzzy graph algorithms and their practical applications.
