Solving the Discrete Multiple Criteria Problem using Convex Cones
提出一种交互式方法，通过成对比较可行解来求解离散确定性多准则问题，适用于具有隐含拟凹递增效用函数的单一决策者。方法利用凸锥消除备选方案，并给出理论证明和数值示例。
An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.