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基于权重难以获知聚类的多准则决策研究

Research on Multi-Criteria Decision-Making Based on Clustering with Hard-to-Know Weights

【作者】 朱旭光;

【导师】 沈玉志;

【作者基本信息】 辽宁工程技术大学 , 管理科学与工程, 2021, 博士

【副题名】以阜新市规上企业土地利用率研究为例

【摘要】 多准则决策理论和方法在土地利用率研究方面应用较为广泛,但所应用的决策方法在指标权重计算时较为粗糙,且难以对结果划分层级,尤其当权重难以获知时。结合聚类分析的多准则决策方法在土地利用率研究中独有千秋,被很多学者采用,但聚类过程亦是需要融合权重数值,在权重难以获知情况下,需要再辟蹊径。权重蕴含着人的信息,人的信息直观表达就是偏好信息,既决策指标的偏好序列,所以可以利用偏好序代替权重。偏序集理论恰能解决偏好序计算问题,亦能胜任利用偏好序进行聚类分析的决策领域。基于此,针对传统研究方法不能解决权重难以获知情况下的决策问题,且难以展示最优解集的层次关系问题,提出了融合偏好序进行聚类的多准则决策方法。首先,针对传统方法不能快速计算出偏好序而只能求权重数值的弊端,提出了基于偏序叠阵计算偏好序的方法,即依据专家判断矩阵,融合全部样本,计算出哈斯矩阵,进而得到偏好序。在构建偏序集并实现多准则决策时,需要考虑数据的分布情况,对于分布不规律的数据,不能单纯利用无量纲化数据构建偏序集,以指标位次构建偏序集进行决策更为可靠。其次,传统多准则决策研究中用到的聚类分析以距离定亲疏关系,需要计算所有样本间距离,针对这种弊端提出了基于偏序集实现有监督学习聚类的多准则决策方法,以成熟的数据集为样本,得到了较好的决策效果;针对传统划分型聚类中种类数难以预知的情况,提出了基于偏序集实现无监督学习聚类的多准则决策方法,能够有效得到簇的数量,亦能较快速实现聚类分析;针对传统多准则决策结果难以展现层次结构的情况,提出了基于偏序集实现层次聚类的多准则决策方法,能够有效展示最优解集的层次关系,为决策者提供了较好决策依据。提出的方法层层递进,即由初探到证实,每一个方法都需要前序章节的支撑。最后,将提出的多准则决策方法,应用于阜新市规上企业土地利用率研究,结合相关分析,得出不同行业土地利用效率决定因素是不同的,有的行业主要取决于使用面积的大小,面积越大一般效率越低,同时土地利用效率与固定资产、主营业收入、建筑密度和税收等几个指标的关系不大。有的行业土地利用效率高低主要取决于建筑面积、主营收入及税收,建筑规模越大、主营收入及税收越高的企业会比建筑规模小、主营收入及税收低的企业的土地利用效率高一些,同时该类行业土地利用效率与固定资产投资和土地面积等指标的关系不大。结果充分说明了提出方法的有效性。该论文有图44幅,表40个,参考文献178篇。

【Abstract】 Multi-criteria-decision-making theory and method are widely used in the research of land use efficiency,but the decision-making method used is rough in the calculation of index weight,and it is difficult to divide the results into levels,especially when the weight is difficult to be known.The multi-criteria-decision-making method combined with cluster analysis is unique in the study of land use efficiency and has been adopted by many scholars.However,the clustering process also needs to integrate the weight values.When the weight is difficult to be known,it is necessary to find another way.Weight contains human information,and the intuitive expression of human information is preference information,which is the preference sequence of decision indicators,so preference order can be used to replace weight.Poset theory can solve the problem of preference order calculation,and can also be competent in the decision-making field of cluster analysis using preference order.Based on this,aiming at the problem that the traditional research methods can not solve the decision-making problem when the weight is difficult to obtain,and it is difficult to show the hierarchical relationship of the optimal solution set,a multi-criteria-decision-making method integrating preference order is proposed.Firstly,under the traditional theoretical framework,it is difficult to quickly calculate the preference order,and only the weight value can be obtained.In view of this disadvantage,a method of calculating the preference order based on the partial order stack matrix is proposed.According to the expert judgment matrix,all samples are fused to generate the partial order stack matrix,calculate the Haase matrix,and then obtain the preference order.When constructing a poset and realizing multi-criteria-decision-making,we need to consider the distribution of data.For the data with irregular distribution,we can not simply use dimensionless data to construct a poset,and it is more reliable to construct a poset with index order for decision-making.Secondly,the clustering analysis used in the traditional multi-criteria-decision-making research determines the relationship between relatives and relatives by distance.Aiming at the need to calculate the distance between all samples in the traditional clustering,a multi-criteria-decision-making method based on poset to realize supervised learning clustering is proposed.Taking the mature data set as the sample,a better decision-making effect is obtained;Aiming at the difficulty of predicting the number of types of traditional partitioned clustering,a multi-criteria-decision-making method based on poset to realize unsupervised learning clustering is proposed,which can not only effectively obtain the number of clusters,but also quickly realize clustering analysis;In view of the difficulty of realizing the hierarchical structure of traditional multi-criteria-decision-making results,a multi-criteria-decision-making method based on hierarchical clustering based on poset is proposed,which can effectively show the hierarchical relationship of the optimal solution set and provide a better decision-making basis for decision-makers.The proposed methods are progressive layer by layer,that is,from preliminary exploration to confirmation,and each method needs the support of the preamble chapters.Finally,the proposed multi-criteria-decision-making method is applied to the study of land use efficiency.Taking Fuxin above designated enterprises as an example,it has achieved good results and can be used as the decision-making basis of relevant departments.Through the analysis of clustering results and correlation analysis,it is concluded that the determinants of land use efficiency in different industries are different.Some industries mainly depend on the size of the use area.The larger the area,the lower the general efficiency.At the same time,the land use efficiency has little relationship with several indicators such as fixed assets,main operating income,building density and tax.The land use efficiency of some industries mainly depends on the construction area,main income and tax.The larger the construction scale,the higher the main income and tax,the land use efficiency of enterprises will be higher than that of enterprises with small construction scale,low main income and tax.At the same time,the land use efficiency of such industries has little relationship with indicators such as fixed asset investment and land area.The results fully show that the proposed method is more suitable for the study of land use efficiency,and can also be applied to other research fields.

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