The Dominance-based Rough Set Approach for analysing patterns of flexibility allocation and design-cost criteria in large-scale irrigation systems

Water planners must provide end-users with reliable and high-quality access to fresh water while complying with financial, institutional, and water availability constraints. In the pursuit of these goals, an over-investment in design can result in stranded assets of significant value and often unwanted environmental implications. Under-investment can lead to supply restrictions affecting human health, the economy, and the environment. The present study uses the Dominance-based Rough Set Approach (DRSA) to develop a balancing strategy concerning complexities encountered in water resource planning for irrigation systems. The methodology relies on the Dominance-based Learning from Examples Module (DOMLEM) algorithm, which extracts minimal set of rules regarding relevant combinations between flexibility allocation and design-cost criteria. The algorithm delineates outcomes in the form of “if., then.” rules that translate decision possibilities facing water planners into: “if (the design is more flexible by this amount), then (we expect this range of cost increment”). Then, a confusion matrix is computed for each irrigation system in order to exclude the rules generating incorrect and ambiguous classification results. The outcome reveals that cost is more subject to elasticity at the hydrant (eh) increment than the network’s coefficient (r). Furthermore, the analysis reveals that the parameter P(q) has only a minor impact on the cost and, as a result, the final decision. Any elasticity (eh) less than 3 assigned to any given coefficient (r) becomes a low-cost increment. For any given value of (eh), the cost increases as the coefficient (r) decrease. Elasticity from 4 to 5 with a network's coefficient (r) equal to or greater than 18/24 becomes a medium-cost increment. Elasticity (eh) from 5 to 6 associated with an (r) equal or less than 16/24 becomes a very high-cost increment. Finally, rather than identifying one solution that seems better than others, this approach provides an interactive schematic that helps identify the appropriate range of flexibility justified by the expense criterion, which allows for debate and supports decision-making.