模糊关系的非循环与负非循环度量

发布时间：2018-01-27 06:00

本文关键词： t-模 t-余模模糊关系非循环指标负非循环指标传递性传递闭包　出处：《太原理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文讨论模糊关系的非循环性与负非循环性的度量,定义并研究了模糊关系的非循环指标以及负非循环指标,从而将文献中的一些非循环与负非循环性质推广为程度描述。模糊关系的非循环指标的研究包括模糊关系的非循环指标及其严格部分的非循环指标两部分。在模糊关系的非循环指标的研究中,我们首先在所涉及的t-模T左连续条件下,讨论了T-非循环指标与T-非对称指标以及T-传递闭包的T-非自反指标之间的关系;其次,在取小t-模下,研究了T-非循环指标与T-传递指标以及T-非自反指标之间的关系。在模糊关系的严格部分的非循环指标的研究中,我们首先在一般的t-模T下,研究了T-非循环指标与其严格部分的T-非循环指标以及T-非对称指标之间的关系;其次,在取小t-模下,讨论了模糊关系的严格部分的min-非循环指标与传递指标之间的关系;最后,讨论了模糊关系的严格部分的min-非循环指标与S-负传递指标之间的关系。接下来是模糊关系的负非循环指标的研究。首先,在一般的t-余模S下,讨论了S-负非循环指标与S-强完全指标的关系;其次,在所涉及的t-余模S右连续的情况下,讨论了S-负非循环指标与S-负传递内部的自反指标之间的关系;最后,在(T,S,n)是De Morgan三元组的条件下,分别研究了模糊关系的S-负非循环指标与其余关系的T-非循环指标之间的关系以及模糊关系的T-非循环指标与其余关系的S-负非循环指标之间的关系。
[Abstract]:This paper discusses the measurement of non cyclic and non cyclic negative fuzzy relation, non circulation index is defined and studied the fuzzy relation and non negative cycle index, and some of the documents of non circulation and non circulation promotion for the degree of negative nature description. Research on non cycle index fuzzy relation includes two parts of non circulation index non cycle index fuzzy relation and its strict part. In the study of non circulation index in the fuzzy relation, we first involved in the t- mode T left continuous conditions, discussed the T- non circulation index and T- index of asymmetry and T- T- non reflexive transitive closure of relations between the indexes; secondly, in the t- mode of T- index and T- index of non cyclic transfer and T- non reflexive relationship between indicators. In the study of non circulation index strictly fuzzy relation in the part, we first in t- T under the general mode, research The T- index and the non circulation strictly part of the T- non cycle index and the relationship between T- index of asymmetry between; secondly, in the small t- mode, discusses the strict part fuzzy relation min- relationship between the non circulation index and transfer index; finally, discusses the strict part of fuzzy relation min- non circulation S- index and negative transfer relations between the indexes. Then study the negative non cycle index of fuzzy relations. First, in general S t- conorms, discussed the relationship between the S- index and S- negative non cyclic strong complete index; secondly, in t- conorm involved S right continuous case the S- and S- non negative cycle index of negative transfer relationship between the reflexive index of the internal; finally, in (T, S, n) De Morgan three tuple conditions, respectively studied the fuzzy relationship between S- index and the relationship between the non negative cycle T- cycle index of the relationship between and The relationship between the T- non cyclic index of the fuzzy relation and the S- negative noncircular index of the other relations.

【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

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