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1. Introduction
Water resources allocation is an important task for distributing water resources to various users for ensuring healthy socioeconomic development and ecoenvironmental protection. The task is especially critical for areas that are currently suffering from water scarcity problems and facing even greater challenges under future climate change. The conflict among different water users is hardly avoidable, but application of management models, that fully consider the uneven spatial and temporal distributions of water resources, the interactions between water supply and demand, and the regulatory requirement of local authorities, will surely benefit the related allocation and planning processes. In recent years, it has been recognized that the intrinsic uncertainties linking with many system components in water resources allocation could also affect the effectiveness of management strategies that are normally made based on deterministic conditions. These uncertainties could be related to water availability (e.g., fluctuating hydrological condition), water demand (e.g., growing population and changing weather), transportation/storage loss, water prices, and even human judgment (e.g., regulatory policies).
The previous research efforts relied heavily on stochastic, fuzzy and interval techniques in tackling uncertainties [1–6]. Among various alternatives, fuzzy mathematical programming (FMP) was found effective in dealing with uncertainties caused by measurement errors, implicit knowledge, and ambiguous human judgment. The definition of the fuzzy parameters in FMP has less strict data requirement than that of stochastic ones, and the fuzzy parameters contain richer distribution information than interval numbers [7, 8]. For decades, many types of FMP models were proposed for solving water resources management problems [9–11]. Depending on the way of handling uncertainties, FMP can be categorized into fuzzy flexible (e.g., fuzzy parametric programming) (FF) [12–14], fuzzy possibilistic (FP) (e.g., fuzzy chance constrained programming) [15–17], and fuzzy robust (FR) [18, 19] programming models. Maqsood...