【作者】 段宝彬；

【导师】 黄健元；

【作者基本信息】 河海大学 ， 应用数学， 2005， 硕士

【摘要】 综合评价问题广泛存在于社会、经济、管理、工程等领域。由于现实世界的大部分事物或现象都具有或多或少的模糊性,因此,处理模糊型不确定性现象的模糊数学方法是解决综合评价问题的重要方法之一。本文针对模糊积分评价模型、模糊优选模型这两种模糊综合评价模型,从理论和实践方面进行了一定的研究,并对两种模型提出了一些改进办法。利用改进后的模型对实际问题进行综合评价,取得了较为理想的效果。 本文得到的主要结论有: 利用(G)模糊积分和Choquet模糊积分的收敛定理,我们得到了关于评分值和重要性测度序列同时收敛的近似客观评价值;将各种单一模糊积分评价值进行加权合成,作为参评对象的最终评价值,在一定程度上弥补了采用单一模糊积分进行综合评价的不足。 对基于模糊一致矩阵的决策方法进行了改进,并将其用于多个参评对象模糊优选时定性指标相对隶属度的计算中;对模糊优选模型中定量指标相对隶属度的计算方法也进行了改进,使得模糊优选的排序结果更为客观、稳定;综合考虑参评对象过去、现在和将来的情况,建立动态多级模糊优选模型,以使评价结果更为全面;目前广泛使用的模糊优选模型通常适用于多个参评对象的排序,本文改进后的模糊优选模型也可用于单个参评对象的综合评价。 总之,本文的研究成果进一步丰富和发展了模糊综合评价的理论和方法。更多还原

【Abstract】 The comprehensive evaluation exists in a lot of fields, such as society, economy, management, project, and etc. Because most things or phenomenon in the real world have fuzziness more or less, so, the fuzzy mathematics method to deal with uncertain phenomenon of fuzzy type turns to be one of the most important methods in comprehensive evaluation. This thesis makes some researches on two kinds of fuzzy comprehensive evaluation models—fuzzy integral evaluation model and fuzzy optimization model, both theorecally and practically. Some improved ways are proposed besides analyzing two kinds of models’ advantage and disadvantage. In the end, the models are applied to practical problems and relative ideal results are reached.In the thesis, the main conclusions are below:By means of convergence theorems of (G) fuzzy integral and Choquet fuzzy integral, the thesis has obtained almost objective appraisal value that converged with respect to sequences of evaluation score and importance measure. Many kinds of single fuzzy integral appraisal values are synthesized to ultimate appraisal value through weighted method to make up the drawback of the single fuzzy integral appraisal value in a degree.The thesis has also improved the calculation of relative membership degree and the decision making method based on fuzzy consistent matrix. Considering the evaluated objects’ situations in the past, the present and the future, we have developed a dynamic fuzzy optimization model. The improved fuzzy optimization model can also be used to the comprehensive evaluation of a single object.In a word, the research results of this thesis enrich and develop the theory and method on fuzzy comprehensive evaluation further.更多还原