广义犹豫模糊软集及其在决策中的应用

发布时间：2018-03-02 19:34

  本文选题：粗糙集　切入点：犹豫模糊软集　出处：《辽宁工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：粗糙集、模糊集还有软集理论都是当代处理不确定性问题的数学工具。经过近些年的发展,三种理论都得到了相继推广,同时,犹豫模糊软集、软模糊粗糙集等以这三种理论为基础的混合型模型也快速地发展起来。根据现有的研究成果,本文对犹豫模糊软集、软模糊粗糙集进一步扩展。首先,在犹豫模糊软集的基础上展开研究,定义广义犹豫模糊软集并研究其相关性质;其次,构建两种广义犹豫模糊软集相似度量方法并应用到实际问题中;最后,对软模糊粗糙集进行推广,建立软犹豫模糊粗糙集模型。具体内容如下:(1)研究广义犹豫模糊软集。在犹豫模糊软集和广义模糊软集理论的基础上,将犹豫模糊软集的参数集赋予犹豫模糊隶属度,构建广义犹豫模糊软集模型;给出广义犹豫模糊软子集的定义;定义一种广义犹豫模糊软集的扩充,可以将参数个数不同的广义犹豫模糊软集转化为参数个数相同的广义犹豫模糊软集;给出广义犹豫模糊软集交、并、补运算的定义,并讨论运算的性质;最后通过算例说明以上定义的合理性。(2)针对广义犹豫模糊软集的相似度量问题,给出其相似度量Ⅰ。首先,在犹豫模糊集包含度的公理化定义基础上,建立犹豫模糊集合的三种包含度公式;利用犹豫模糊集的三种包含度公式构造出犹豫模糊集的三种相似度公式;其次依照犹豫模糊集相似度量的公理化定义给出广义犹豫模糊软集相似度量的公理化定义,并利用犹豫模糊集的三种相似度公式构造广义犹豫模糊软集的相似度公式,同时对该公式加以证明;最后利用广义犹豫模糊软集相似度量Ⅰ构建一种决策方法,并将其应用到环境治理问题中。(3)针对广义犹豫模糊软集的相似度量问题,给出其相似度量Ⅱ。首先,在犹豫模糊集包含度的公理化定义基础上,给出广义犹豫模糊软集包含度的公理化定义,并利用犹豫模糊集合的三种包含度公式构造出广义犹豫模糊软集间的包含度公式;然后从广义犹豫模糊软集的包含度出发来构造广义犹豫模糊软集的相似度公式,这种相似度的计算方法同样适用于参数集不同的广义犹豫模糊软集;最后将广义犹豫模糊软集的相似度Ⅱ应用到关于城市饮水卫生评价的聚类分析实例中,通过实例说明了所提出方法的可行性。(4)提出双论域上的犹豫模糊粗糙集,并讨论其性质;研究软犹豫模糊粗糙集,给出软犹豫模糊粗糙集上近似和下近似算子,并讨论其性质;构建基于软犹豫模糊粗糙集的决策算法并将其应用到购买汽车的决策问题中;最后讨论软犹豫模糊粗糙集模型与广义犹豫模糊软集模型的联系,对两种模型在汽车买卖问题中的实际意义做出说明。
[Abstract]:Rough set, fuzzy set and soft set theory are mathematical tools for dealing with uncertain problems in modern times. Through the development of recent years, three kinds of theories have been popularized one after another, at the same time, hesitant fuzzy soft sets, The hybrid models based on these three theories have also developed rapidly. According to the existing research results, this paper further extends the hesitant fuzzy soft sets and soft fuzzy rough sets. On the basis of hesitating fuzzy soft set, the paper defines generalized hesitant fuzzy soft set and studies its related properties. Secondly, two kinds of similarity measure methods of generalized hesitation fuzzy soft set are constructed and applied to practical problems. This paper generalizes soft fuzzy rough set and establishes soft hesitating fuzzy rough set model. The concrete contents are as follows: 1) the generalized hesitating fuzzy soft set is studied. On the basis of the theory of hesitating fuzzy soft set and generalized fuzzy soft set, The parameter set of the hesitating fuzzy soft set is given the membership degree of the hesitation fuzzy, the model of the generalized hesitant fuzzy soft set is constructed, the definition of the generalized hesitant fuzzy soft subset is given, and the extension of the generalized hesitant fuzzy soft set is defined. The generalized hesitation fuzzy soft set with different parameter number can be transformed into the generalized hesitation fuzzy soft set with the same parameter number, the definition of the intersection of the generalized hesitation fuzzy soft set and the complement operation is given, and the properties of the operation are discussed. Finally, an example is given to illustrate the rationality of the above definition.) for the similarity measurement problem of generalized hesitant fuzzy soft sets, the similarity measure is given. First, on the basis of the axiomatic definition of the inclusion degree of the hesitating fuzzy set, Three kinds of inclusion degree formulas of hesitant fuzzy sets are established, and three similarity formulas of hesitant fuzzy sets are constructed by using the three inclusion degree formulas of hesitating fuzzy sets. Secondly, according to the axiomatic definition of similarity measure of hesitating fuzzy set, the axiomatic definition of similarity measure of generalized hesitation fuzzy soft set is given, and the similarity formula of generalized hesitation fuzzy soft set is constructed by using three similarity formulas of hesitating fuzzy set. At the same time, the formula is proved. Finally, a decision method is constructed by using the similarity measure I of generalized hesitant fuzzy soft sets, and applied to the problem of environmental governance. First of all, based on the axiomatic definition of the inclusion degree of the hesitating fuzzy set, the axiomatic definition of the inclusion degree of the generalized hesitating fuzzy soft set is given. By using the three kinds of inclusion degree formulas of the hesitating fuzzy set, the inclusion degree formula of the generalized hesitant fuzzy soft set is constructed, and the similarity formula of the generalized hesitant fuzzy soft set is constructed from the inclusion degree of the generalized hesitating fuzzy soft set. This similarity calculation method is also suitable for generalized hesitant fuzzy soft sets with different parameter sets. Finally, the similarity 鈪，

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