多粒度覆盖粗糙直觉模糊集模型的研究

发布时间：2018-10-13 07:49

【摘要】：粗糙集理论是Pawlak教授提出的处理不准确、不完整和不明晰信息的数学方法。模糊集理论是Zadeh教授提出的,用来刻画模糊现象以及模糊概念的数学工具。其后,Atanassov教授推广了Zadeh教授的模糊集理论,并在模糊集理论的基础之上,给出了直觉模糊集的概念,该理论给出了隶属度同时,又给出了非隶属度和犹豫度的概念,既表达了“亦此亦彼”,也表达了“非此非彼”的现象。在分析处理不明确、不完备等信息时,直觉模糊集相较于模糊集具有更强表达能力。由于直觉模糊集和粗糙集理论在处理不明确性和不完整性问题时,考虑问题出发角度与侧重方向不是相同的,两个理论具有很强的互补性。于是,Dubois创造性地将这两种理论结合起来进行研究,两种理论的融合已经成为了新的研究热点,引起了许多学者的研究兴趣。近几年,覆盖粗糙集、邻域粗糙集、多粒度粗糙集是粗糙集的重要拓展形式,它们的研究引起了许多学者的关注,成为新的研究热点。目前,将覆盖粗糙集和直觉模糊集的结合、邻域粗糙集与直觉模糊集的结合,同时从粒度的角度对它们的研究成果较少,对其进行研究具有一定的理论价值和实际意义。因此本文在覆盖理论基础上,对粗糙集、邻域粗糙集以及直觉模糊集结合进行了研究,并从粒度的角度出发,对覆盖粗糙直觉模糊集拓展进行了研究,建立了一些模型,研讨了这些模型的一些重要性质,并用算例验证了有效性。本文的创新点如下:(1)在粗糙集、直觉模糊集和覆盖理论基础上,给出了模糊覆盖粗糙隶属度和非隶属度的定义,构建了一种新的模型----覆盖粗糙直觉模糊集,证明了该模型的一些重要性质,与此同时又定义了一种新的直觉模糊集的相似性度量公式,并用例子进行了验证;(2)把最小描述由单一粒度拓展到了多个粒度,提出了新的基于多粒度的最小描述定义。在此基础上,给出了多粒度的模糊覆盖粗糙隶属度、非隶属度概念,构建了I型、II型多粒度覆盖粗糙直觉模糊集模型,讨论了它们的性质,并举例说明;(3)基于不同的属性集序列和不同的邻域半径,定义了双重粒化准则,建立基于双重粒化准则的多粒度邻域粗糙直觉模糊集模型。并给出该模型的相关性质。然后,提出了乐观与悲观多粒度邻域粗糙直觉模糊集的近似集,并讨论了这些模型的一些重要性质,最后由例子验证了这些模型的有效性。
[Abstract]:Rough set theory is a mathematical method proposed by Professor Pawlak to deal with inaccurate, incomplete and unclear information. Fuzzy set theory is a mathematical tool for describing fuzzy phenomena and fuzzy concepts proposed by Professor Zadeh. After that, Professor Atanassov generalizes Professor Zadeh's fuzzy set theory and gives the concept of intuitionistic fuzzy set on the basis of fuzzy set theory. It not only expresses the phenomenon of "this is also that", but also expresses the phenomenon of "neither this nor that". The intuitionistic fuzzy sets have stronger expressive ability than fuzzy sets in analyzing and dealing with uncertain and incomplete information. Because the intuitionistic fuzzy set and rough set theory are different from each other when dealing with the problem of uncertainty and incompleteness, the two theories are highly complementary. Therefore, Dubois creatively combines the two theories to study. The fusion of the two theories has become a new research hotspot, which has aroused the interest of many scholars. In recent years, covering rough sets, neighborhood rough sets and multi-grained rough sets are important extension forms of rough sets. At present, the combination of covering rough set and intuitionistic fuzzy set, the combination of neighborhood rough set and intuitionistic fuzzy set, and the research results of them from the angle of granularity have certain theoretical value and practical significance. Therefore, on the basis of covering theory, this paper studies the combination of rough set, neighborhood rough set and intuitionistic fuzzy set, and studies the extension of covering rough intuitionistic fuzzy set from the angle of granularity, and establishes some models. Some important properties of these models are discussed, and the validity of these models is verified by an example. The innovations of this paper are as follows: (1) on the basis of rough set, intuitionistic fuzzy set and covering theory, the definitions of fuzzy covering rough membership degree and non-membership degree are given, and a new model, covering rough intuitionistic fuzzy set, is constructed. Some important properties of the model are proved. At the same time, a new similarity measurement formula of intuitionistic fuzzy sets is defined and verified by an example. (2) the minimum description is extended from single granularity to multiple granularity. A new definition of minimum description based on multi-granularity is proposed. On this basis, the concepts of multi-granularity fuzzy covering rough membership degree and non-membership degree are given, and I type, II type multi-granularity covering rough intuitionistic fuzzy set model are constructed, and their properties are discussed. An example is given to illustrate. (3) based on different attribute set sequences and different neighborhood radius, double granulation criteria are defined, and a multi-granularity neighborhood rough intuitionistic fuzzy set model based on double granulation criteria is established. The related properties of the model are given. Then, the approximate sets of rough intuitionistic fuzzy sets with optimistic and pessimistic multi-granularity neighborhood are proposed, and some important properties of these models are discussed. Finally, the validity of these models is verified by an example.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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