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Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences

by 1, 1,* and 2,3
1
Business School, Hohai University, Nanjing 211100, China
2
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
3
Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
*
Author to whom correspondence should be addressed.
Sustainability 2019, 11(4), 1099; https://doi.org/10.3390/su11041099
Received: 6 January 2019 / Revised: 9 February 2019 / Accepted: 14 February 2019 / Published: 19 February 2019
(This article belongs to the Section Economic and Business Aspects of Sustainability)
An incomplete fuzzy preference framework for the Graph Model for Conflict Resolution (GMCR) is proposed to handle both complete and incomplete fuzzy preference information. Usually, decision makers’ (DMs’) fuzzy preferences are assumed to be complete fuzzy preference relations (FPRs). However, in real-life situations, due to lack of information or limited expertise in the problem domain, any DM’s preference may be an incomplete fuzzy preference relation (IFPR). An inherent advantage of the proposed framework for GMCR is that it can complete the IFPRs based on additive consistency, which is a special form of transitivity, a common property of preferences. After introducing the concepts of FPR, IFPR, and transitivity, we propose an algorithm to supplement IFPR, that is, to find an FPR that is a good approximation. To illustrate the usefulness of the incomplete fuzzy preference framework for GMCR, we demonstrate it using to a real-world conflict over water allocation that took place in the Zhanghe River basin of China. View Full-Text
Keywords: water resource allocation; graph model for conflict resolution; incomplete fuzzy preferences; additive transitivity water resource allocation; graph model for conflict resolution; incomplete fuzzy preferences; additive transitivity
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MDPI and ACS Style

Wu, N.; Xu, Y.; Kilgour, D.M. Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences. Sustainability 2019, 11, 1099. https://doi.org/10.3390/su11041099

AMA Style

Wu N, Xu Y, Kilgour DM. Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences. Sustainability. 2019; 11(4):1099. https://doi.org/10.3390/su11041099

Chicago/Turabian Style

Wu, Nannan, Yejun Xu, and D. M. Kilgour. 2019. "Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences" Sustainability 11, no. 4: 1099. https://doi.org/10.3390/su11041099

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