Multi-Dimensional Vector Space Decision Model and Its Application for Multi-Objective Operation Risk Analysis of Reservoirs

The multi-objective operation of reservoirs is impacted by several uncertainties, thus there are many difficulties to determine the optimal operation scheme under a given acceptable risk level. In this paper, improvements are made to optimize the traditional vector space model, and then the multi-dimensional vector space decision model is proposed to enhance the significant difference of evaluation results. To accomplish this, firstly, structuring the proposed schemes by non-inferior solutions of the multi-objective operation risk analysis model; secondly, obtaining the mapping distance between the vector of the proposed schemes and that of the ideal one. Next, we develop an optimal vector space decision model for multi-objective operation risk analysis of reservoirs. Finally, the feasibility and effectiveness of the model are verified by results of an example. The methodology in this paper proves simple and clear, with a particularly noteworthy advantage in terms of the distinctiveness among computed results.