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The α-Representation Inexact T2 Fuzzy Sets Programming Model for Water Resources Management of the Southern Min River Basin under Uncertainty

1
College of Environmental Science and Engineering, Xiamen University of Technology, Xiamen 361024, China
2
Department of Civil Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada
3
School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
4
Environmental Systems Engineering Program, University of Regina, Regina, SK S4S 0A2, Canada
*
Authors to whom correspondence should be addressed.
Symmetry 2018, 10(11), 579; https://doi.org/10.3390/sym10110579
Received: 7 October 2018 / Revised: 18 October 2018 / Accepted: 23 October 2018 / Published: 2 November 2018
In this study, a new α-representation of the inexact T2 fuzzy sets programming model (α-RITF2SP) is proposed for water resources planning under uncertainties. The developed model is a hybrid of inexact type-2 (T2) fuzzy sets (FSs) optimal programming based on α-cuts and α-planes (z-slices) algorithms, and both can be used in problems of water resource management without a loss of generality. Therefore, this novel method represents a complementary method to combine both of these algorithms to make inexact T2FSs methods easier and faster for users under uncertainties. This method provides not only a reduction in computations when computing fuzzy functions, but also a map of the primary variable of T2FSs in the secondary membership function. The α-RITF2SP is applied to a real case study of the operation of water resource systems in the southern Min River basin that involves three cities: Xiamen, Zhangzhou, and Quanzhou. The results of the water allocations and benefits have been analyzed. The symptoms of results indicate the higher profit with a higher wastewater treatment rate. It also represents that this model has enhanced abilities and it is relevant and practical as well as can serve as a guide for the development of this regional economy. View Full-Text
Keywords: water resources; type 2 fuzzy sets; α-cuts; α-planes; uncertainty water resources; type 2 fuzzy sets; α-cuts; α-planes; uncertainty
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MDPI and ACS Style

Jin, L.; Fu, H.; Kim, Y.; Wang, L.; Cheng, H.; Huang, G. The α-Representation Inexact T2 Fuzzy Sets Programming Model for Water Resources Management of the Southern Min River Basin under Uncertainty. Symmetry 2018, 10, 579. https://doi.org/10.3390/sym10110579

AMA Style

Jin L, Fu H, Kim Y, Wang L, Cheng H, Huang G. The α-Representation Inexact T2 Fuzzy Sets Programming Model for Water Resources Management of the Southern Min River Basin under Uncertainty. Symmetry. 2018; 10(11):579. https://doi.org/10.3390/sym10110579

Chicago/Turabian Style

Jin, Lei, Haiyan Fu, Younggy Kim, Li Wang, Huiyan Cheng, and Guohe Huang. 2018. "The α-Representation Inexact T2 Fuzzy Sets Programming Model for Water Resources Management of the Southern Min River Basin under Uncertainty" Symmetry 10, no. 11: 579. https://doi.org/10.3390/sym10110579

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