模糊关系的非循环性与负非循环性
发布时间：2019-03-17 09:32
【摘要】：本文定义了模糊关系的非循环性与负非循环性,并对其性质进行了详细地研究。对模糊关系的T-非循环性研究包括模糊关系的T-非循环性及其严格部分的T-非循环性.对模糊关系非循环性的研究包括:首先,在T左连续下,讨论了T-非循环性与T-传递闭包及其非自反性的关系;其次,在取小t-模下,讨论了minT-非循环性与其截集的非循环性之间的关系.对模糊关系严格部分的T-非循环性的研究包括:首先,讨论了T-非循环性与其严格部分T-非循环性以及T-非对称性之间的关系;其次,在所涉及的t-模是左连续和n_T是强非的条件下,给出了严格部分T-非循环性的一个等价陈述;然后,在左连续t-模下,研究了严格部分T-非循环性与T-传递的关系;最后,在左连续t-模和De Morgan三元组的条件下,研究了严格部分的T-非循环性与SS-负传递的关系。然后,我们对模糊关系的S-负非循环性进行了讨论,包括模糊关系的S-负非循环性及与T-非循环性之间的关系.在所涉及的t-余模是右连续的情况下,讨论了S-负非循环性与S-负传递内部及其自反性的关系.对模糊关系负非循环性与非循环关系的研究包括:首先,在取小t-模、取大t-余模下,研究了S-负非循环性与严格部分的T-非循环性的关系;然后,在De Morgan三元组下,讨论了S-负非循环性与严格部分的T-非循环性及其余关系的T-非循环性之间的关系。
[Abstract]:In this paper, the non-circularity and negative non-circularity of fuzzy relations are defined, and their properties are studied in detail. The study of Tacyclic property of fuzzy relation includes the Tacyclic property of fuzzy relation and the Tacyclic property of strict part of fuzzy relation. The research on the non-circularity of fuzzy relations includes: firstly, the relationship between T-acyclic property and T-transitive closure and its non-reflexivity is discussed under T-left continuous condition; Secondly, under the small t-module, we discuss the relationship between the non-circularity of minT- and the non-circularity of its truncated set. The research on Tacyclic property of strict part of fuzzy relation includes: firstly, the relationship between Tacyclic property and its strict part Tacyclic property as well as Tasymmetry is discussed. Secondly, an equivalent statement of the strictly partial T-acyclic property is given under the condition that the t-modules involved are left-continuous and the n-T is strongly non-cyclic. Then, under the left continuous t-module, the relation between strictly partial T-acyclic property and T-transfer is studied. Finally, under the condition of left continuous t-module and De Morgan triple, the relation between the T-acyclic property of strict part and the negative transfer of SS- is studied. Then, we discuss the S-negative non-circularity of fuzzy relations, including the S-negative non-circularity of fuzzy relations and the relationship between S-negative non-circularity and T-non-circularity of fuzzy relations. In this paper, the relation between S-negative acyclic property and S-negative transitive interior and its reflexivity is discussed when the t-comodule involved is right-continuous. The research on negative non-circularity and acyclic relation of fuzzy relation includes: firstly, the relation between S-negative acyclic property and strict part of T-acyclic property is studied under the condition of taking small t-module and large t-comodule, and the relation between S-negative acyclic property and strict part of T-acyclic property is studied. Then, under the De Morgan triple, the relations between the S-negative acyclic property, the strict part Tacyclic property and the other relations of the Tacyclic property are discussed.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
本文编号：2442158
[Abstract]:In this paper, the non-circularity and negative non-circularity of fuzzy relations are defined, and their properties are studied in detail. The study of Tacyclic property of fuzzy relation includes the Tacyclic property of fuzzy relation and the Tacyclic property of strict part of fuzzy relation. The research on the non-circularity of fuzzy relations includes: firstly, the relationship between T-acyclic property and T-transitive closure and its non-reflexivity is discussed under T-left continuous condition; Secondly, under the small t-module, we discuss the relationship between the non-circularity of minT- and the non-circularity of its truncated set. The research on Tacyclic property of strict part of fuzzy relation includes: firstly, the relationship between Tacyclic property and its strict part Tacyclic property as well as Tasymmetry is discussed. Secondly, an equivalent statement of the strictly partial T-acyclic property is given under the condition that the t-modules involved are left-continuous and the n-T is strongly non-cyclic. Then, under the left continuous t-module, the relation between strictly partial T-acyclic property and T-transfer is studied. Finally, under the condition of left continuous t-module and De Morgan triple, the relation between the T-acyclic property of strict part and the negative transfer of SS- is studied. Then, we discuss the S-negative non-circularity of fuzzy relations, including the S-negative non-circularity of fuzzy relations and the relationship between S-negative non-circularity and T-non-circularity of fuzzy relations. In this paper, the relation between S-negative acyclic property and S-negative transitive interior and its reflexivity is discussed when the t-comodule involved is right-continuous. The research on negative non-circularity and acyclic relation of fuzzy relation includes: firstly, the relation between S-negative acyclic property and strict part of T-acyclic property is studied under the condition of taking small t-module and large t-comodule, and the relation between S-negative acyclic property and strict part of T-acyclic property is studied. Then, under the De Morgan triple, the relations between the S-negative acyclic property, the strict part Tacyclic property and the other relations of the Tacyclic property are discussed.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
【参考文献】
相关期刊论文 前2条
1 李欣;王绪柱;;关于t-模的旋转不变性[J];模糊系统与数学;2015年06期
2 秦效英;韩红娟;;模糊关系的S-负传递内部的研究[J];太原理工大学学报;2006年04期
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