A Two-Step Infinite α-Cuts Fuzzy Linear Programming Method in Determination of Optimal Allocation Strategies in Agricultural Irrigation Systems

A two-step infinite α-cuts fuzzy linear programming (TSIFP) method is developed in this study. The introduction of infinite α-cuts to conventional fuzzy linear programming frameworks makes it possible to generate more reliable optimal results than conventional fuzzy linear programming, where finite α-cuts were assumed to be sufficient in representing all fuzzy information of the membership functions. In contrast to the previous studies, the proposed TSIFP can be noted as the first attempt in solving FLP without any unreasonable simplification and assumption. An agricultural irrigation system is then provided for demonstrating its applicability. The results show that reasonable solutions and allocation strategies are obtained. As a typical finite α-cuts fuzzy linear programming method, fuzzy robust linear programming (FRLP) is further considered to solve the same problem; results from this method are then compared with those from TSIFP. It is indicated that, due to the constraints being relaxed in FRLP, more water beyond the system’s capacity would be over-allocated for pursuing higher system benefits, implying the unreliability of FRLP in being extended to real-world practices. Two scenario analyses under different α-level cutting means for FRLP are also investigated.