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

Abstract

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.

Study on the Optimization of Multi-Objective Water Resources Allocation in the Henan Yellow River Water Supply Zone

“…However, due to the complexity of water allocation, it is often necessary to use mathematical analytical models to integrate different categories of information for calculation and comprehensive evaluation in order to obtain programmatic results that can be used as a reference for decision making. Traditional approaches to solving mathematical planning models include linear programming methods, nonlinear programming, stochastic linear programming, and dynamic programming [19][20][21][22]. However, with the multi-objective and multi-variable nature and high dimensionality of current water resources allocation models, the traditional optimization algorithms are not very effective in terms of convergence, computational efficiency, parameter sensitivity, etc.…”