Abstract: The comprehensive evaluation model represented by partial order set can transform the complete rational paradigm of evaluation into the finite rational paradigm, and then improve the ability of the model to deal with uncertainty and reduce the evaluation risk. On the basis of partial order set theory, the full order weight is extended to partial order weight, and the partial order representation of evaluation function under partial weight sequence is solved. The generalized representation theorem of partial order sets shows that the function expressed in partial order can be valued as fuzzy number, fuzzy hesitation value, interval number, random number and so on. The results show that the comprehensive evaluation of partial order representation solves the problem of empowerment completely and fully expresses the personal preference of decision makers. From the perspective of the operation effect of the model, the range of data processed by the model is increased, the evaluation result is more robust and reliable, and the structured information between schemes is presented through Hasse graph, which has the function of layering and clustering.

Key words: comprehensive evaluation, poset, partial order relation, weight

摘要： 偏序集表示的综合评价模型能将从完全理性范式转换为有限理性范式,进而提升模型应对不确定性的能力,识别评价风险。在偏序集理论的基础上,将权重拓展为偏序权重,解决了部分权重序列条件下评价函数的偏序表示问题。偏序集广义表示定理表明了,偏序表达的函数可以为模糊数、模糊犹豫值、区间数、随机数等多种取值。结果表明:偏序表示的综合评价彻底解决了赋权难题,且充分表达了决策者的个人偏好。从模型运行效果来看,模型处理数据范围增加、评价结果更加稳健可靠,并通过Hasse图展现了方案间的结构化信息,具有分层和聚类的功能。

关键词: 综合评价, 偏序集, 偏序关系, 权重