【作者】 陈娜；

【导师】 徐泽水；

【作者基本信息】 东南大学 ， 管理科学与工程， 2015， 博士

【摘要】 随着现代经济与社会的发展,人们所考虑问题的模糊性和不确定性不断增强。犹豫模糊集是Torra和Narukawa于2010年提出的处理决策和聚类问题中所遇到的模糊性的强有力工具,它允许一个元素属于一个集合的隶属度为几个可能的值。因此,犹豫模糊集提供了一种适当的方式来表达决策者在给出评估信息时出现的犹豫性。本论文研究了犹豫模糊环境下的决策和聚类问题,取得以下主要结果：(1)首次把犹豫模糊集拓展到区间犹豫模糊集。定义了区间犹豫模糊集和区间犹豫模糊数的概念,研究了相应的数学运算性质并给出了相关的集成算子和距离测度。建立了区间犹豫模糊偏好关系,提出了可用于决策者权重已知和未知情况下基于区间犹豫模糊偏好信息的决策方法,它们能直观地考虑不同决策者意见的差异。(2)提出了基于ELECTRE的犹豫模糊多属性决策方法,推广了ELECTRE方法的应用范围。定义了偏离函数概念,并结合得分函数和偏离函数给出了犹豫模糊数的比较准则；定义了犹豫模糊环境下的一致集和不一致集概念,并构建了方案间的级别占优关系；提出了基于ELECTRE Ⅰ和ELECTRE Ⅱ的犹豫模糊多属性决策方法。(3)提出了基于指派模型的犹豫模糊多属性决策方法。通过犹豫模糊数的比较法则,我们构建了能考虑属性权重的加权偏好序频矩阵,进而提出了基于指派模型的犹豫模糊以及区间犹豫模糊多属性决策方法,这些新方法能给出方案的完整序。此外,构造了基于犹豫模糊数和区间犹豫模糊数的指派问题模型,并给出其求解方法。(4)给出了犹豫模糊环境下的聚类算法。建立了犹豫模糊集和区间犹豫模糊集的关联系数公式和关联矩阵；给出了基于等价关联矩阵的犹豫模糊聚类算法。此外,在犹豫模糊信息集成算子和距离测度的基础上,结合层次聚类和K-均值聚类这两种算法,提出了对犹豫模糊信息进行聚类的算法。更多还原

【Abstract】 With the development of modern economy and society, the fuzziness and uncertainty of the decision making problems that people consider have been enhanced significantly. Hesitant fuzzy sets (HFSs), which were proposed by Torra and Narukawa in 2010, are a powerful tool of handling the fuzziness encountered in decision making and clustering issues. The new concept allows the membership degree of an element to a set represented by several possible values. Therefore, HFSs provide a suitable manner to express hesitancy when decision makers give their evaluation values for alternatives. This paper focuses on the study of decision making methods and clustering algorithms under hesitant fuzzy environments. The main results obtained in our work are as follows:(1) The HFSs are extended to interval-valued hesitant fuzzy sets (IVHFSs). We define the concepts of IVHFS and interval-valued hesitant fuzzy element, explore the corresponding properties of mathematical operations and present relevant aggregation operators and distance measures. We establish interval-valued hesitant fuzzy preference relations, based on which we propose the decision making methods for the cases where the weights of the decision makers are known and unknown, which can intuitively address the difference in evaluation information given by the decision makers.(2) The hesitant fuzzy multi-attribute decision making methods based on the ELECTREs (ELimination Et Choix Traduisant la Realite) are proposed, and thus, the application domain of the ELECTREs is extended. We define the concept of deviation function and combine it with score function to give comparison laws for hesitant fuzzy elements (HFEs). We formulate outranking relations among alternatives using the concepts of concordance and discordance under hesitant fuzzy environments, and develop the hesitant fuzzy decision making methods based on ELECTRE I and ELECTRE II respectively.(3) The hesitant fuzzy multi-attribute decision making methods based on the assignment models are given. By means of the comparison laws for HFEs, we formulate a weighted preference ranking frequency matrix that accounts for the weights of attributes, and propose the hesitant fuzzy and interval-valued hesitant fuzzy decision making methods using the assignment models, which can give a total order of alternatives. In addition, we develop the assignment models based on HFEs and interval-valued hesitant fuzzy elements (IVHFEs), and give the corresponding methods to solve the developed models.(4) The algorithms are given for clustering hesitant fuzzy information. We establish the correlation coefficient formula and the correlation matrix for HFSs and IVHFSs, and give the hesitant fuzzy clustering algorithms using equivalent hesitant fuzzy correlation matrix. In addition, on the basis of the aggregation operators and distance measures for hesitant fuzzy information, we propose the hierarchical hesitant fuzzy K-means algorithm by combining both the hierarchical clustering algorithm and the K-means clustering algorithm.更多还原