基于格值逻辑的模糊代数研究

发布时间：2018-04-13 14:23

本文选题：剩余格 + t-滤子　；参考：《江南大学》2016年硕士论文

【摘要】：模糊逻辑研究的一个重要方向是研究其逻辑代数系统.逻辑代数系统中一般以偏序集和一些运算为模型来建立逻辑与代数的桥梁,用代数方法解决逻辑问题.剩余格是一类比较重要的代数系统.本文探讨了剩余格上的t-滤子、I-滤子、EIMTL-滤子等滤子的性质,给出剩余格上n-维模糊滤子、n-维模糊EIMTL-滤子、n-维模糊t-滤子、n-维模糊同余关系的定义,还研究了它们的性质.取得的主要结果概括如下：在第二章中,讨论了t-滤子和I-滤子的关系.将EIMTL-滤子和associative滤子的定义推广到剩余格并研究了它们的性质,讨论了在什么条件下,EIMTL-滤子一定是t-滤子.证明了每个剩余格都有真EIMTL-滤子.另外,还讨论了剩余格满足什么条件有真associative滤子.最后将EIMTL-滤子定义推广到非可换剩余格,并研究了它的性质.在第三章中,将剩余格上一维模糊模糊滤子概念进行推广给出了n-维模糊滤子的概念,并讨论了它的等价刻画,讨论了n-维模糊滤子与其上截集的关系.给出了n-维模糊EIMTL-滤子的概念,并讨论了它的等价刻画,也讨论了n-维模糊EIMTL-滤子与其上截集的关系.给出了n-维模糊t-滤子的概念,并研究了它的性质,运用n-维模糊t-滤子,得到n-维模糊divisible滤子和n-维模糊strong滤子的定义及其刻画.在第四章中,给出剩余格上n-维模糊同余关系定义,并研究它的一些性质.引入n-维模糊关系的上截集定义,并且讨论它与n-维模糊同余关系的关系.给出剩余格上n-维模糊滤子和n-维模糊同余关系的一一对应.还讨论了n-维模糊等价关系与其α-水平关系的关系.
[Abstract]:An important research direction of fuzzy logic is to study its logic algebraic system.In the logic algebra system, the partial ordered set and some operations are generally used as the models to build the bridge between logic and algebra, and the algebraic method is used to solve the logic problem.Residual lattices are a class of more important algebraic systems.In this paper, we discuss the properties of n-dimensional fuzzy filters on residual lattices, and give the definitions of n-dimensional fuzzy t- filters and n-dimensional fuzzy t- filters on residual lattices, and study their properties.The main results are summarized as follows: in chapter 2, the relationship between t- filter and I- filter is discussed.The definitions of EIMTL-filter and associative filter are generalized to residual lattices and their properties are studied. The conditions under which EIMTL-filters must be tfilters are discussed.It is proved that every residual lattice has true EIMTL- filter.In addition, we also discuss what conditions the residual lattices satisfy to have true associative filters.Finally, the definition of EIMTL- filter is extended to non-commutative residuals and its properties are studied.In chapter 3, we generalize the concept of one-dimensional fuzzy filter on residual lattices, give the concept of n-dimensional fuzzy filter, discuss its equivalent characterization, and discuss the relation between n-dimensional fuzzy filter and its upper cut set.In this paper, the concept of n-dimensional fuzzy EIMTL-filter is given, its equivalent characterization is discussed, and the relation between n-dimensional fuzzy EIMTL-filter and its upper cut set is also discussed.In this paper, the concept of n-dimensional fuzzy tfilters is given, and its properties are studied. By using n-dimensional fuzzy tfilters, the definitions and characterizations of n- dimensional fuzzy divisible filters and n- dimensional fuzzy strong filters are obtained.In chapter 4, we give the definition of n-dimensional fuzzy congruence relation on residual lattices and study its properties.This paper introduces the definition of upper cut set of n-dimensional fuzzy relation and discusses its relation with n-dimensional fuzzy congruence relation.The one-to-one correspondence between n-dimensional fuzzy filters and n-dimensional fuzzy congruences on residual lattices is given.The relationship between the n- dimensional fuzzy equivalence relation and its 伪-level relation is also discussed.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O159

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