The linear Diophantine fuzzy set (LDFS) incorporates two reference parameters, thereby enabling a more comprehensive representation of human judgment. This structure provides flexibility, as the decision-maker can adjust the meaning of the reference parameters to reflect changes in the decision context. Among the many applications of fuzzy sets, information measures such as distance and entropy are particularly significant. Entropy is widely employed in objective attribute-weighting procedures of Multiple Attribute Decision Making (MADM) applications, as it captures the intrinsic information content of attributes. So, the first contribution of this study is the development of a new entropy measure for LDFS. Besides, the second contribution is the extension of the Proximity Indexed Value (PIV) method into the LDFS framework, marking the first proposal of LDF-oriented PIV in the literature. PIV was selected due to its flexibility, ease of application, and the proven strength against the rank reversal phenomenon. The proposed entropy measure is integrated into the attribute-weighting procedure of this new LDF-En-PIV extension. The third contribution is an application-oriented decision model for the selection of green suppliers with respect to their performance in building and employing an ISO14001 Environmental Management System. In this case study, four green supplier alternatives were evaluated across the main components of ISO14001 by a panel of experienced industry experts, with rankings obtained through the LDF-En-PIV approach. The robustness of the proposed approach was presented through comparative analyses with crisp PIV and LDF-ARAS. All comparisons yield consistent rankings, demonstrating the reliability of the proposed approach.
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