基于优化模型的乘性偏好关系一致性改进算法

Consistency Improving Algorithm for Multiplicative Preference Relation Based on Optimization Model

针对乘性偏好信息下的决策问题,引入乘性偏好关系的有序一致性、满意一致性以及一致性指数等概念,建立以偏差变量最小化为目标函数的优化模型,进而构建基于乘性偏好关系一致性的决策方案优劣关系排序算法,并证明迭代算法收敛。该决策算法在满足一定条件下能够利用乘性偏好关系的有序一致性特征快速有效地做出决策,同时能够运用最小非负偏差变量对非一致性乘性偏好关系进行一致性调整,使得调整后的乘性偏好关系满足满意一致性条件,从而得到决策方案的排序向量,最终使得决策者获得合理可靠的决策结果。通过综合补给船的选择实验说明该决策算法是合理有效的。

In view of the decision making problems with multiplicative preference information, the order consistency, acceptable consistency and consistency index of multiplicative preference relation are introduced. An optimization model is developed with the principle of minimum non-negative deviation variables. An algorithm to derive the ranking of alternatives in decision making is investigated based on the consistency of multiplicative preference relation. The main characteristics of the proposed algorithm are that：It helps decision makers make decision quickly and efficiently by using the properties of the order consistent multiplicative preference relation. It repairs the consistency of multiplicative preference relation by using the optimal deviation values and ensures that the repaired multiplicative preference relation is acceptable consistent. The priority weight vector is obtained, and it helps the decision maker to obtain the reasonable and reliable decision making results. A practical application to selection of comprehensive replenishment ship is demonstrated to show the rationality and effectiveness of the proposed algorithm.