模糊蕴涵构造方法的研究

发布时间：2018-06-03 20:46

本文选题：模糊逻辑 + 模糊蕴涵　；参考：《浙江理工大学》2017年硕士论文

【摘要】：模糊蕴涵作为一种重要的逻辑算子被广泛应用于诸多领域,如模糊推理,模糊控制,模糊图像处理,词计算,模糊数学形态学,数据挖掘等.正是由于它的理论意义与应用价值,近年来关于模糊蕴涵算子的研究受到关注,其研究热点主要集中于:模糊蕴涵构造方法的研究,模糊蕴涵性质的分析与刻画,以及模糊蕴涵与一些函数方程的关系.本文将提出模糊蕴涵新的构造方法,并将研究由这些方法生成的模糊蕴涵的性质与它们满足一些函数方程的条件.全文的主要内容如下:Vemuri与Jayaram提出了模糊蕴涵的两种合成方法,但它们不保持序性质与换质位对称性.为了弥补这一不足,我们提出模糊蕴涵另一种新的合成方法及其推广,证明了这两种合成方法都保持序性质与换质位对称性.并对新生成的两类模糊蕴涵具有的其它性质也进行了讨论.通过利用(0,1)中一组严格单调增序列,将模糊蕴涵水平e-阈值生成方法与垂直e-阈值生成方法作了有意义的推广,我们分别称这两种方法为模糊蕴涵水平多阈值生成方法与垂直多阈值生成方法.分析水平多阈值生成的模糊蕴涵与垂直多阈值生成的模糊蕴涵的一些性质且对它们进行了刻画.讨论水平多阈值生成的模糊蕴涵与一些函数方程之间的关系.通过利用T-模,T-余模与模糊否定N提出了模糊蕴涵三种换质位对称化的新方法,分别称为(T,N)-换质位对称化,(S,N)-换质位对称化和(T,S,N)-换质位对称化.由这三种方法得到的三类模糊蕴涵分别关于强否定具有换质位对称性.此外对这三类模糊蕴涵所具有的其它性质也进行了详细讨论.基于不满足恒等原则与序性质的模糊蕴涵,我们提出模糊蕴涵的两种修正方法,使得修正后的模糊蕴涵分别满足这两个性质,并对修正后的模糊蕴涵所保持的其它性质也进行探究.
[Abstract]:As an important logic operator, fuzzy implication is widely used in many fields, such as fuzzy reasoning, fuzzy control, fuzzy image processing, word computing, fuzzy mathematical morphology, data mining and so on. It is precisely because of its theoretical significance and application value that the research on fuzzy implication operators has attracted much attention in recent years. The research focus is mainly on the research of fuzzy implication construction methods, the analysis and characterization of fuzzy implication properties. And the relation between fuzzy implication and some functional equations. In this paper, a new construction method of fuzzy implication is proposed, and the properties of fuzzy implication generated by these methods and the conditions for them to satisfy some functional equations are studied. The main contents of this paper are as follows: 1. The composition methods of fuzzy implication proposed by: Vemuri and Jayaram, but they do not maintain the properties of order and the symmetry of transposition. In order to remedy this deficiency, we propose another new synthesis method with fuzzy implication and its generalization. It is proved that both of the two methods maintain the order property and the symmetry of transposition. The other properties of the two newly generated fuzzy implication are also discussed. By using a group of strictly monotone increasing sequences, this paper generalizes the fuzzy implication horizontal e- threshold generation method and the vertical e- threshold generation method. We refer to these two methods as fuzzy implication horizontal multi-threshold generation method and vertical multi-threshold generation method respectively. Some properties of fuzzy implication generated by horizontal multi-threshold and vertical multi-threshold are analyzed and characterized. The relationship between the fuzzy implication generated by horizontal multi-threshold and some functional equations is discussed. In this paper, three new methods of translocation symmetry of fuzzy implication are proposed by using T- mod T- comodules and fuzzy negative-N, which are called "T _ (T)" -T ~ (+) ~ (1) -S ~ (1) -N ~ (+) -N ~ (+) -N ~ (+) -T _ (1) -T _ (1) and T ~ (+) _ (S) _ (N) The three kinds of fuzzy implication obtained from these three methods are respectively about strong negation with transposable symmetry. In addition, the other properties of these three kinds of fuzzy implication are also discussed in detail. Based on the fuzzy implication which does not satisfy the identity principle and the order property, we propose two modified methods of fuzzy implication, so that the modified fuzzy implication satisfies these two properties respectively. The other properties of the modified fuzzy implication are also discussed.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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