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

• Main Authors: Lei Jin, Haiyan Fu, Younggy Kim, Li Wang, Huiyan Cheng, Guohe Huang
• Format: Article
• Language: English
• Published: MDPI AG 2018-11-01
• Series: Symmetry
• Subjects: water resources; type 2 fuzzy sets; <i>α</i>-cuts; <i>α</i>-planes; uncertainty
• Online Access: https://www.mdpi.com/2073-8994/10/11/579

In this study, a new <i>&#945;</i>-representation of the inexact T2 fuzzy sets programming model (<i>&#945;</i>-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 <i>&#945;</i>-cuts and <i>&#945;</i>-planes (<i>z</i>-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 <i>&#945;</i>-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.