Control Theory & Systems
Ali Dehghani Filabadi; Hossein Nahid Titkanlue
Abstract
This paper addresses multi-attribute group decision-making (MAGDM) where linguistic assessments are represented by both positive and negative interval type-2 fuzzy numbers (IT2FNs), capturing the intrinsic uncertainty of group evaluations more accurately. We introduce a novel ranking method ...
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This paper addresses multi-attribute group decision-making (MAGDM) where linguistic assessments are represented by both positive and negative interval type-2 fuzzy numbers (IT2FNs), capturing the intrinsic uncertainty of group evaluations more accurately. We introduce a novel ranking method for IT2FNs that simultaneously utilizes the mean and standard deviation of the upper and lower membership functions, as well as the IT2FN's height. This enhances its discriminatory capability. The theoretical foundations of this ranking— encompassing zero, unity, and symmetry properties— are rigorously established, and its superiority over existing techniques is demonstrated through comparative analyses on seven benchmark datasets. Building on this ranking, we develop an integrated fuzzy MAGDM framework that can handle both positive and negative IT2FN assessments for criteria and weights. The framework’s practicality and effectiveness are validated through two case studies: one with exclusively positive linguistic terms and another with mixed positive and negative scales. Results indicate that the proposed ranking and decision framework yield more rational and robust group decisions under substantial uncertainty. They outperform conventional fuzzy methods and offer a nuanced solution for real-world MAGDM scenarios.
Control Theory & Systems
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.
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