A Green Supplier Selection Through an MCDM Based Framework Under Fuzzy Environment

Ting-Yu Lin, Kuo-Chen Hung (), Josef Jablonsky and Kuo-Ping Lin
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Ting-Yu Lin: Department of Industrial Engineering and Enterprise Information, Tunghai University, Taichung City 407224, Taiwan
Kuo-Chen Hung: Department of Multimedia Game Development and Application, Hungkuang University, Taichung City 433304, Taiwan
Josef Jablonsky: Department of Econometrics, Prague University of Economics and Business, 120 00 Prague, Czech Republic
Kuo-Ping Lin: Department of Industrial Engineering and Enterprise Information, Tunghai University, Taichung City 407224, Taiwan

Mathematics, 2025, vol. 13, issue 3, 1-31

Abstract: Uncertainty exists in reality decision-making problems. Therefore, fuzzy theories, fuzzy intervals, intuitionistic fuzzy, and Z-numbers have been proposed and successfully applied to multi-criteria decision-making (MCDM). However, since the information presented in the Z-numbers method is the subjective opinion of the decision-maker, the problem of overestimating or underestimating the reliability of the information may occur in both individual and group decision-making. The Extended Z-numbers (Z E -numbers) method was proposed in 2021 to solve this problem; hence, the decision-making process no longer relies on subjective opinions only but seeks external experts related to the problem to further vote on the evaluation value given by the internal decision-maker, in order to modify the information’s reliability, and thus to obtain a more realistic result. This paper combines the Z E -numbers method with the improved Elimination et Choix Traduisant la Realite II (ELECTRE II) proposed in 2022 and proposes a new MCDM method based on Z E -numbers, named Z E -ELECTRE II. The green supplier selection problem was used as an illustrative example. Meanwhile, the close analysis in this paper examines two primary dimensions of variability: (1) simulation of external expert voting situations to analyze the variations in information reliability and decision-making results and to cross-compare them with other MCDM methods; (2) investigation of the impact of internal preferences, as reflected through systematic adjustments to the weights of the evaluation criteria. The results show that uncertainty of information, reliability, and the perspectives of different decision-makers and expert groups can be considered through Z E -numbers. The proposed Z E -ELECTRE II is applicable to group decision-making, validates the robustness of the process, and is suitable for dynamic decision-making under varying decision-maker preferences. Furthermore, using the Z E -numbers along with the MCDM method can obtain more flexibility and more reliable results.

Keywords: improved ELECTRE II; Z-numbers; extend Z-numbers; Z E –ELECTRE II; decision science; green supplier selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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