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Open AccessFeature PaperArticle

Multi-Criteria Group Decision-Making for Selection of Green Suppliers under Bipolar Fuzzy PROMETHEE Process

1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 77; https://doi.org/10.3390/sym12010077
Received: 10 December 2019 / Revised: 27 December 2019 / Accepted: 29 December 2019 / Published: 2 January 2020
The preference ranking organization method for enrichment of evaluations (PROMETHEE) method considers a significant outranking class of multi-criteria decision analysis (MCDA), as it is easy to deal with its simple computations. In the PROMETHEE, different preference functions are used according to the type and nature of attributes or criteria that demonstrate the clearness and reliability of this method. This study provides a new version of the PROMETHEE method using bipolar fuzzy information, named the bipolar fuzzy PROMETHEE method. Bipolar fuzzy sets or numbers constitute an asymmetrical relationship between two judgmental factors of human reasoning. Vague and imprecise knowledge is characterized by bipolar fuzzy linguistic terms which are further represented in the form of trapezoidal bipolar fuzzy numbers. The trapezoidal bipolar fuzzy numbers are used by analysts to assign the preferences of alternatives on the basis of criteria. Further, a ranking function of bipolar fuzzy numbers is considered to access the crisp real preferences of alternatives. The entropy weighting information is employed to calculate the weights of attributes by considering the condition of normality. A numerical example such as the selection of green suppliers by using the bipolar fuzzy PROMETHEE is performed on the basis of the usual criterion preference function in order to explain the procedure of the proposed method. Comparable results are derived by using the combination of linear and level preference functions. The results obtained by using different types of preference functions are the same, representing the authenticity of the proposed bipolar fuzzy PROMETHEE method. View Full-Text
Keywords: trapezoidal bipolar fuzzy numbers; PROMETHEE; preference functions; green supplier selection trapezoidal bipolar fuzzy numbers; PROMETHEE; preference functions; green supplier selection
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MDPI and ACS Style

Akram, M.; Shumaiza; Al-Kenani, A.N. Multi-Criteria Group Decision-Making for Selection of Green Suppliers under Bipolar Fuzzy PROMETHEE Process. Symmetry 2020, 12, 77.

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