FI代数上的直觉模糊滤子和同余关系及格蕴涵代数上的两种直觉模糊滤子

发布时间：2018-03-20 22:13

本文选题：模糊集　切入点：直觉模糊集　出处：《陕西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：为了研究与人类思维模式更相近的模糊推理方法,美国学者K.T.Atanassov定义了直觉模糊集这一概念.由于直觉模糊集在实际应用中展现出巨大的潜力,因此得到了众多学者的亲睐,在短短的几十年间,有关直觉模糊集的理论取得了累累硕果.直觉模糊集的研究已经涉及到决策分析、人工智能、拓扑、逻辑代数等诸多领域.其中在逻辑代数领域里,有关学者把模糊滤子和直觉模糊集结合在一起,引入了直觉模糊滤子的概念.本文的第一部分在FI代数中引入了直觉模糊滤子的概念,并利用直觉模糊滤子诱导出FI代数上的一种同余关系,进一步研究了它的基本性质,期待这些工作对FI代数结构的研究起到一定的促进作用.自从Menger于1942年引入T-模的概念以后,它已经被应用到多个领域,其中包括概率度量空间、半群理论、函数方程理论、模糊逻辑理论等.本文的第二部分将在裴峥研究的格蕴涵代数中的直觉模糊滤子的基础上,将直觉模糊滤子与T-模相结合,引入了T1,T2直觉模糊滤子和T1,T2直觉模糊关联滤子的概念,分别研究了T1,T2直觉模糊滤子和T1,T2直觉模糊关联滤子的相关性质并给出了等价刻画,期待这些工作为进一步研究格蕴涵代数上的其他滤子提供了一定的参考.本文主要内容及安排如下：第一章预备知识.主要介绍了本文所涉及的与FI代数和格蕴涵代数相关的概念、例子和结论.第二章FI代数上的直觉模糊滤子和同余关系.在FI代数上引入了直觉模糊滤子的概念,给出了FI代数上直觉模糊滤子的一个等价刻画,并由直觉模糊滤子出发定义了它上的一个同余关系,并讨论了它的一些简单性质.第三章格蕴涵代数上的两种直觉模糊滤子.将直觉模糊滤子与T-模相结合应用到格蕴涵代数中,给出了两种直觉模糊滤子的定义,分别研究了它们的性质并给出了等价刻画.
[Abstract]:In order to study the fuzzy reasoning method which is more similar to the human thinking mode, the American scholar K.T. Atanassov defined the concept of intuitionistic fuzzy set. Because of the great potential of intuitionistic fuzzy set in practical application, it has been favored by many scholars. In just a few decades, the theory of intuitionistic fuzzy sets has made a lot of achievements. The research of intuitionistic fuzzy sets has been related to many fields, such as decision analysis, artificial intelligence, topology, logic algebra and so on. Some scholars combine fuzzy filter with intuitionistic fuzzy set and introduce the concept of intuitionistic fuzzy filter. The first part of this paper introduces the concept of intuitionistic fuzzy filter in fi algebra. A congruence relation on fi algebras is induced by using intuitionistic fuzzy filters, and its basic properties are further studied. Since Menger introduced the concept of T-norm in 1942, it has been applied to many fields, including probabilistic metric space, semigroup theory, function equation theory. The second part of this paper combines intuitionistic fuzzy filters with T-modules on the basis of intuitionistic fuzzy filters in lattice implication algebras studied by Pei Zheng. The concepts of T 1 T 2 intuitionistic fuzzy filter and T 1 T 2 intuitionistic fuzzy correlation filter are introduced. The correlation properties of T 1 T 2 intuitionistic fuzzy filter and T 1 T 2 intuitionistic fuzzy correlation filter are studied and the equivalent characterizations are given. It is expected that these works will provide a certain reference for the further study of other filters on lattice implication algebras. The main contents and arrangements of this paper are as follows: the first chapter is the preparatory knowledge. The concepts associated with algebra, In chapter 2, we introduce the concept of intuitionistic fuzzy filters on fi algebras, and give an equivalent characterization of intuitionistic fuzzy filters on fi algebras. A congruence relation on the intuitionistic fuzzy filter is defined. Some simple properties of it are discussed. In the third chapter, two kinds of intuitionistic fuzzy filters on lattice implication algebras are discussed. The combination of intuitionistic fuzzy filters and T-modules is applied to lattice implication algebras, and the definitions of two intuitionistic fuzzy filters are given. Their properties are studied and the equivalent characterizations are given.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O159;O144

【参考文献】