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犹豫模糊语言术语集的熵及其在决策中的应用

发布时间:2018-12-14 07:36
【摘要】:犹豫模糊语言术语集能够灵活、全面地反映决策者的定性决策信息,在供应链管理、模式识别和医疗诊断等领域具有广泛的应用前景,已成为模糊集理论研究中的热点.熵是用来衡量模糊信息的不确定性,是模糊集理论中一个重要研究内容.本论文研究犹豫模糊语言术语集和带概率的犹豫模糊语言术语集的熵,并提出一种基于熵测度和离平均方案(平均解)距离(EDAS)的犹豫模糊语言多属性决策方法.本文一共分为三章.第一章,介绍犹豫模糊语言术语集和带概率的犹豫模糊语言术语集及其熵理论的研究背景、发展现状及相关的预备知识.第二章,研究犹豫模糊语言术语集的熵和基于熵的EDAS决策方法.首先定义犹豫模糊语言术语集的模糊性指标和犹豫性指标,并在此基础上给出犹豫模糊语言术语集的二元熵(包含模糊熵和犹豫熵)的公理化定义,给出构建模糊熵和犹豫熵的一般方法和具体的熵公式.之后,提出一个综合熵公式,该公式能够综合反映犹豫模糊语言术语集的模糊性和犹豫性特征.对提出的熵公式,结合具体的数据与现有的熵公式进行了比较,说明其合理性与优越性.最后,提出一种基于熵和EDAS的决策方法,用以解决属性权重未知的犹豫模糊语言多属性决策问题.第三章,研究带概率的犹豫模糊语言术语集的熵.提出带概率的犹豫模糊语言术语集的熵的公理化定义,并给出熵公式的构造方法和具体的熵公式.提出的熵公式既能反映带概率的犹豫模糊语言术语集的模糊性,又能反映其犹豫性,因此能全面地刻画其不确定性.最后,用具体的多属性决策实例说明所提出的熵公式在多属性群决策中的应用.
[Abstract]:The term set of hesitating fuzzy language can flexibly reflect the qualitative decision information of decision makers. It has wide application prospects in the fields of supply chain management, pattern recognition and medical diagnosis, and has become a hot spot in the research of fuzzy set theory. Entropy is used to measure the uncertainty of fuzzy information and is an important research content in fuzzy set theory. In this paper, we study the entropy of the hesitancy fuzzy language terminology set and the hesitant fuzzy language terminology set with probability, and propose a multi-attribute decision making method based on entropy measure and distance from the average solution (EDAS). This paper is divided into three chapters. In the first chapter, we introduce the background, the present situation and the related preparatory knowledge of the hesitant fuzzy language terminology set and the probabilistic hesitant fuzzy language terminology set and its entropy theory. In chapter 2, the entropy of hesitant fuzzy terminology set and the EDAS decision method based on entropy are studied. Firstly, the fuzziness index and hesitancy index of hesitating fuzzy language terminology set are defined, and then the axiomatic definition of binary entropy (including fuzzy entropy and hesitating entropy) of hesitant fuzzy language terminology set is given. The general method of constructing fuzzy entropy and hesitating entropy and the specific entropy formula are given. After that, a comprehensive entropy formula is proposed, which can reflect the fuzziness and hesitancy characteristics of the hesitant fuzzy language terminology set. The proposed entropy formula is compared with the existing entropy formula in combination with the specific data, which shows its rationality and superiority. Finally, a decision method based on entropy and EDAS is proposed to solve the problem of uncertain fuzzy language multi-attribute decision making with unknown attribute weight. In chapter 3, we study the entropy of the hesitant fuzzy language terminology set with probability. The axiomatic definition of entropy in the set of hesitant fuzzy terms with probability is proposed, and the method of constructing entropy formula and the specific entropy formula are given. The proposed entropy formula can not only reflect the fuzziness of the set of hesitant fuzzy terms with probability, but also reflect its hesitancy, so it can describe its uncertainty comprehensively. Finally, an example of multi-attribute decision making is given to illustrate the application of the proposed entropy formula in multi-attribute group decision making.
【学位授予单位】:扬州大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O159;O225

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