Optimization & Operations Research
Harmandeep Kaur; Sukhpreet Kaur Sidhu
Abstract
Multi-criteria decision-making (MCDM) often involves situations characterized by uncertainty, ambiguity, and vagueness. To address such complexities, MCDM techniques play a crucial role. This paper presents a comparative analysis of two widely used methods—Technique for Order Preference by ...
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Multi-criteria decision-making (MCDM) often involves situations characterized by uncertainty, ambiguity, and vagueness. To address such complexities, MCDM techniques play a crucial role. This paper presents a comparative analysis of two widely used methods—Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR)—within a hesitant fuzzy environment. Hesitant fuzzy sets allow decision-makers to express hesitation by assigning multiple possible membership values to an element rather than a single value. In this framework, the TOPSIS ranks alternatives based on their closeness to the positive and negative ideal solutions, while the VIKOR identifies a compromise solution by balancing individual and collective regret measures. The effectiveness of the comparison is demonstrated through illustrative numerical examples. Moreover, some real life applications of these methods are discussed.
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.
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