一种基于非传递广义全序的多目标决策方法

THE NEW MULTIOBJECTIVE DECISION MAKING METHOD BASED ON THE GENERALIZED INTRANSITIVE TOTAL ORDERING

本文通过定义点一集映射H_β锥而建立了一种非传递广义全序H_β-序,在此序基础上建立了一个等价关系,实现了对决策问题目标空间的等价划分及对等价类的优先排序。本文证明了在这一等价划分下,H_β-序是一个全序关系。将H_β-序应用于多目标决策(MODM)问题,本文提出了一种解决MODM问题的新方法,这一方面适用于有限备选方案的决策情况,特别适应目标间的关系错综复杂,难以进行效用归并的场合。与现有基于排序的MODM方法相比,本文的方法更具有一般性,而且保证了收敛于全局满意解。

A kind of generalized intransitive total ordering, H_β-ordering, is established based on the point-to-set mapping H_β-cone in this paper. An equivalent relation is obtained on the basis of the ordering, by which the objective space of the multiobjective decision making (MODM) problems can be divided into rankable equivalent classes. It is proved that H_β-ordering is a kind of total ordering relation under the division. Applying this relation as ranking criterion to MODM problems, a new method is introduced. The method is applicable to limited-alternatives MODM problems, especially appropriate to cases with high complexity of relations among objectives, which is hardly solvable by means of combining the utilities. Compared with the previous approaches, this one is more general and comprehensive, and guarantees the obtainment of the global preferred solution.