模糊粗糙集理论及其在群中的应用

发布时间：2018-06-29 16:37

本文选题：模糊子集 + 粗糙集　；参考：《聊城大学》2017年硕士论文

【摘要】：不确定性问题在我们的实际生产生活中是普遍存在的,而模糊集理论、粗糙集理论均适于解决处理信息系统中的不确定性问题.粗糙集理论、模糊集理论经过几十年的发展,均形成了相对完备的理论体系.而我国学者取得了重要的研究成果,并受到国内外学者的广泛关注.本文主要研究了模糊粗糙集的基本性质.在处理现实中越来越复杂的信息时,为了更好地进行处理、筛选、分类找到对我们有用的信息,我们可以借助模糊粗糙集与粗糙模糊集模型来处理这些复杂的信息问题.所以本文所做的工作主要包括以下四个方面:第一,在群中,我们可以由模糊集理论得到的模糊子群,通过与粗糙集理论相结合,研究粗糙模糊子群,并构造出该群中子集的下、上近似算子,我们研究了这个模型中的关于模糊代数方面的一些基本性质.第二,在群中,借助一个模糊关系,可以在这个代数关系中生成一个模糊近似空间.进而构造出一个新的模糊粗糙集模型.研究了这个新模型中的一个上、下近似算子的结构性质,即这个模糊子群的模糊正规子群.第三,在粗糙集上,我们可以通过覆盖的关系,定义在这个基础上的新模型,并且可以进一步讨论研究这个基于覆盖的模糊粗糙集新模型的一些基本的相关的代数性质.第四,借助模糊集的表现定理,通过集合套,构造出了一种新的多粒度模糊粗糙集的模型,并且构造出此模型中的下、上近似.由这个模型的上、下近似还得到了一些有趣的结论.本文的这些研究成果使得在代数系统中的模糊粗糙集理论与粗糙模糊集的理论更为成熟与丰富,并为以后的关于此方面的代数研究提供了更有力的条件.
[Abstract]:Uncertainty problems are common in our actual production and life, while fuzzy set theory and rough set theory are all suitable for solving uncertainty problems in information processing systems. After decades of development, rough set theory and fuzzy set theory have formed a relatively complete theoretical system. Chinese scholars have made important research results, and have received extensive attention from domestic and foreign scholars. In this paper, the basic properties of fuzzy rough sets are studied. In order to deal with more and more complex information in reality, we can deal with these complex information problems by means of fuzzy rough set and rough fuzzy set model in order to better process, filter and classify the useful information for us. So the work of this paper mainly includes the following four aspects: first, in the group, we can get the fuzzy subgroup from the fuzzy set theory, by combining with the rough set theory, we study the rough fuzzy subgroup. The lower and upper approximation operators of the subsets in the group are constructed. We study some basic properties of fuzzy algebras in this model. Secondly, a fuzzy approximate space can be generated in this algebraic relation by means of a fuzzy relation in a group. Then a new fuzzy rough set model is constructed. In this paper, we study the structural properties of an upper and lower approximation operator in this new model, that is, the fuzzy normal subgroup of the fuzzy subgroup. Thirdly, we can define a new model on rough set by covering relation, and we can further study some basic algebraic properties of the new fuzzy rough set model based on covering. Fourthly, by means of the representation theorem of fuzzy sets, a new model of multi-granularity fuzzy rough sets is constructed by means of set jackets, and the lower and upper approximations of this model are constructed. Some interesting conclusions are also obtained from the upper and lower approximations of this model. These results of this paper make the theory of fuzzy rough sets and rough fuzzy sets more mature and rich in algebraic systems, and provide more powerful conditions for further algebraic research in this field.
【学位授予单位】：聊城大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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