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In realistic water resource planning, fuzzy constraints can be violated but still allowed to certain acceptance degrees. To address this issue, in this study, a bi-objective pseudo-interval type 2 (T2) linear programming approach with a ranking order relation between the intervals is proposed for water system allocation. This developed approach can transform normal T2 fuzzy sets, including both trapezoidal and triangular types, into the bi-objective linear programming approach solved with the proposed algorithm with mathematical rigor, which improves the flexibility of the decision supports. The new model is applied in the utilization of regional water resource management in Xiamen city, China. Concurrently, a local water system model is established by considering the aspects of industrial, agricultural, and municipal requirements. Thus, by analysis of the solution algorithm, decision-makers can obtain different optimal results by selecting different acceptance degrees. The results also demonstrate the superiority of the proposed method. Therefore, this approach not only augments the theory of the optimal allocation method in water resource management, but also provides the support for meeting the requirements of the 13th five-year plan for Xiamen ecological planning.

A Bi-Objective Pseudo-Interval T2 Linear Programming Approach and Its Application to Water Resources Management Under Uncertainty