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<p>The linear Diophantine fuzzy (LDF) set enhances traditional fuzzy sets by incorporating two control parameters that better capture human judgment. This LDF provides deciders with the flexibility to handle decision-making scenarios by altering the interpretation of these control parameters. Fuzzy set information metrics are commonly used in decision making, where distance–similarity metrics rank alternatives based on how close they are to ideal or average solutions. This study introduces a new distance-based similarity metric for linear Diophantine fuzzy set (LDFS), thoroughly examining its attributes. The proposed metric is shown to outperform existing LDFS metrics in the literature. Additionally, the study adapts the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to the LDFS framework, resulting in the innovative LDF–TOPSIS method. A key development in this study is the creation of a decision model for selecting smart farming technologies, where five alternatives were evaluated against six criteria by three experts using LDF–TOPSIS method. Lastly, the proposed similarity metric is applied to clustering analysis, demonstrating its practical utility by providing more insightful and effective outcomes.</p>

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Linear Diophantine Fuzzy Similarity Measure with Applications to TOPSIS and Clustering Analysis

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • K. M. Abirami,
  • R. Srikanth,
  • P. Dhanasekaran

摘要

The linear Diophantine fuzzy (LDF) set enhances traditional fuzzy sets by incorporating two control parameters that better capture human judgment. This LDF provides deciders with the flexibility to handle decision-making scenarios by altering the interpretation of these control parameters. Fuzzy set information metrics are commonly used in decision making, where distance–similarity metrics rank alternatives based on how close they are to ideal or average solutions. This study introduces a new distance-based similarity metric for linear Diophantine fuzzy set (LDFS), thoroughly examining its attributes. The proposed metric is shown to outperform existing LDFS metrics in the literature. Additionally, the study adapts the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to the LDFS framework, resulting in the innovative LDF–TOPSIS method. A key development in this study is the creation of a decision model for selecting smart farming technologies, where five alternatives were evaluated against six criteria by three experts using LDF–TOPSIS method. Lastly, the proposed similarity metric is applied to clustering analysis, demonstrating its practical utility by providing more insightful and effective outcomes.