犹豫模糊集间的序关系及其在多属性决策中的应用

发布时间：2018-07-09 23:51

本文选题：犹豫模糊集 + 序关系　；参考：《广西大学》2017年硕士论文

【摘要】：多属性决策问题普遍存在于社会生活的各个方面,它不仅包含国家战略性的决策,如中国的南水北调、修建三峡大坝等;还涵盖人们的日常安排,如旅行计划、理财产品的选择等.多属性决策问题的目的是根据决策信息从多个具备相同属性的方案中选择出最佳方案.由于决策问题、决策环境的复杂性和人类思维的模糊性,决策者通常采用区间数、三角模糊数、梯形模糊数、直觉模糊数、犹豫模糊集等来描述不确定决策信息.而犹豫模糊集描述犹豫不决情形下的不确定决策信息具有优势,能反映真实的决策情形,因此,本文对犹豫模糊环境下的多属性决策方法的研究具有重要的理论意义和实际意义.主要内容如下:(1)犹豫模糊集的序关系是根据犹豫模糊信息进行决策的关键.本文从犹豫模糊集的序关系入手,分析现有序关系下的决策技术存在的缺陷,包括缺乏柔性、决策信息丢失等.为了克服这些缺陷,本文重新构建了犹豫模糊集之间的序关系——可能度和优先度,并研究其具备的性质,包括规范性、互补性、弱传递性等.新的序关系能够尽可能的保持决策信息的完整性,避免决策信息丢失.(2)基于本文提出的犹豫模糊集序关系(可能度和优先度),研究了犹豫模糊环境下的多属性决策模型,并将基于本文提出的序关系下的多属性决策方法与传统决策技术进行比较,论证其有效性与合理性.(3)在犹豫模糊语言环境中,本文构造了一类新的犹豫模糊语言术语集的距离测度,并相应地拓展出了犹豫模糊语言术语间序关系构造模型,包括 Hamming、Euclidean 和 Hausdorff 等距离测度.本文对犹豫模糊环境下的多属性决策方法研究将有利于完善多属性决策理论,丰富不确定决策的理论与方法.
[Abstract]:The problem of multi-attribute decision-making is common in all aspects of social life. It includes not only the strategic decisions of the country, such as the South-to-North Water transfer in China, the construction of the three Gorges Dam, and so on; it also covers people's daily arrangements, such as travel plans. Selection of financial products, etc. The purpose of multi-attribute decision making problem is to select the best scheme from many schemes with the same attributes according to the decision information. Due to the decision problems, the complexity of the decision-making environment and the fuzziness of human thinking, decision makers usually use interval numbers, triangular fuzzy numbers, trapezoidal fuzzy numbers, intuitionistic fuzzy numbers, hesitant fuzzy sets to describe uncertain decision information. And the uncertain decision information in the case of indecision is described by the hesitant fuzzy set, which has the advantage of reflecting the real decision situation, so, This paper is of great theoretical and practical significance to the study of multi-attribute decision making in uncertain fuzzy environment. The main contents are as follows: (1) the order relation of the hesitant fuzzy set is the key to the decision based on the hesitant fuzzy information. Starting with the order relation of hesitant fuzzy sets, this paper analyzes the shortcomings of the existing decision technology under the order relation, including the lack of flexibility, the loss of decision information, and so on. In order to overcome these defects, this paper reconstructs the order relation between hesitant fuzzy sets-possibility degree and priority degree, and studies its properties, including normative, complementary, weak transitivity and so on. The new order relation can keep the integrity of decision information as far as possible and avoid the loss of decision information. (2) based on the order relation (possibility degree and priority degree) proposed in this paper, the multi-attribute decision making model in hesitating fuzzy environment is studied. In this paper, the method of multi-attribute decision making based on the order relation is compared with the traditional decision making technology to prove its validity and rationality. (3) in the environment of hesitant fuzzy language, In this paper, we construct a class of distance measures for a new set of hesitant fuzzy language terms, and accordingly extend the model of order relation between hesitant fuzzy language terms, including Hammingli Euclidean and Hausdorff isometric measures. In this paper, the study of multi-attribute decision making method in hesitant fuzzy environment will be helpful to perfect the theory of multi-attribute decision making and enrich the theory and method of uncertain decision making.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159;O225

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