MCDM problem under single-valued neutrosophic numbers based on a novel similarity measure

Madineh Farnam ¹ ( Department of Electrical Engineering, Shohadaye Hoveizeh Campus of Technology, Shahid Chamran University of Ahvaz, Dasht-e Azadegan, Khuzestan, Iran. )
Majid Darehmiraki ² ( Department of Mathematics and Statistics, Faculty of Data Sciences and Energy, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran. )

Submited date : 2024-09-18 Accepted date : 2025-02-11

Keywords: Neutrosophic set, Single-valued Neutrosophic number, Ranking methods, Similarity measure, Multi-criteria decision making.,

Abstract :

One of the challenges in MCDM with a neutrosophic environment is the lack of an efficient analysis tool to rank the alternatives. The effective ranking of alternatives in MCDM under a neutrosophic environment presents a significant challenge due to the absence of robust analytical tools. Bridging this gap is essential for enhancing decision-making processes across various practical applications. Aggregative operators, ranking methods, distance measures, and similarity measures are among the most essential tools for sorting fuzzy data and their extensions, including Neutrosophic numbers. However, existing methods often exhibit significant shortcomings, such as contradictory results under certain conditions, and computational inefficiency. For example, Deli and Subas’s approach and Ye’s approach may yield contradicting results for specific instances of single-valued trapezoidal neutrosophic (SVTriN) numbers. The novel similarity measure proposed in this study introduces a new mathematical formulation that enhances the meaningfulness and conceptual soundness of the analysis by effectively capturing the intrinsic indeterminacy of neutrosophic numbers. Unlike existing methods, it provides consistent results across various scenarios, eliminating contradictory outcomes. This innovative approach deepens the understanding of relationships between alternatives, making it highly suitable for practical implementation in MCDM problems. On the other hand, very few papers have used the similarity measure to sort the alternatives in the MCDM problem under trapezoidal neutrosophic numbers. Thus, the main objective of this study is to introduce a novel similarity measure for sorting alternatives. For this purpose, we first highlight some shortcomings related to the existing ranking approach for neutrosophic numbers. After introducing the novel similarity measure, several critical properties of the suggested similarity measure between neutrosophic numbers are investigated. The proposed similarity measure offers a proper way to apply the TOPSIS method in the context of neutrosophic information. The efficiency and utility of the proposed similarity measure are illustrated by a comparative example.

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