On the Properties of Fuzzy Switching Functions

Abstract

A strictly binary approach to the treatment of switching circuits today is not always adequate to describe systems in the real world. This approach is partly due, to the relative simplicity of designing binary switching systems, and to the fact that basic switching modules in common use are two-positional. Consequently, every variable in Boolean logic is assumed to be two-valued. However, because of real-world constraints, the attributes of system variables are often ambiguously defined. In other words, quite often variables might have values other than falsehood and truth. Cases with such attributes arise, for example in artifical intelligence and related subjects. Ever since Zadeh introduced the idea of fuzzy set theory [11 by utilizing the concept of membership grade, a number of authors have been concerned with the analysis and applications of fuzzy models. Especially, the relation of fuzzy to switching systems have been discussed in [2]–[12] and by other researchers in relation to other topics.

In this paper we are concerned with the study of fuzzy switching functions and their properties. Special attention is devoted to their minimization, enumeration, and their application to Boolean static hazard detection.     

A Note on Fuzzy Probability of a Fuzzy Event

This article modifies evaluating the probability of a fuzzy event based on a classical probability space introduced by Yager (Inform. Sci. 1979;18:113–122). The presented theoretical results will be illustrated with some propositions and remarks. It is shown that a modification in the definition of fuzzy probability of fuzzy events into a concept of such probabilities has some desirable properties from mathematical points of view. Then, the proposed fuzzy probability will be compared to that of the similar proposed methods. The proposed fuzzy probability will be illustrated with some numerical examples.     

A Survey on Fuzzy Implication Functions

One of the key operations in fuzzy logic and approximate reasoning is the fuzzy implication, which is usually performed by a binary operator, called an implication function or, simply, an implication. Many fuzzy rule based systems do their inference processes through these operators that also take charge of the propagation of uncertainty in fuzzy reasonings. Moreover, they have proved to be useful also in other fields like composition of fuzzy relations, fuzzy relational equations, fuzzy mathematical morphology, and image processing. This paper aims to present an overview on fuzzy implication functions that usually are constructed from t-norms and t-conorms but also from other kinds of aggregation operators. The four most usual ways to define these implications are recalled and their characteristic properties stated, not only in the case of [0,1] but also in the discrete case.     

关于模糊系统研究的认识和评价以及其它

首先 ,十分感谢孙增圻与胡包刚教授组织的“模糊控制与模糊系统”专刊 (见《自动化学报》第 2 7卷第四期 ) .专刊中的许多高水平的文章 ,加深了近年来自己“还没有年轻过 ,就已经老了”的感觉 .但最引起我兴趣的 ,还是王立新博士的文章《模糊系统 :挑战与机遇并存——十年研究之感悟》[1 ] (以下简称《感悟》) .记得第一次与立新见面 ,是 1992年在图森的 IEEE CDC(决策与控制 )会议上 .那时 ,我在亚利桑那大学教书 ,立新也已去伯克利作博士后 .或许是因为我的导师 Saridis和立新的导师 Mendel是好朋友 ,大家很快就开诚布公地谈了许多对…     

复合控制一种简便模糊切换方法

针对常见的FUZZY—PI和FUZZY-PID等复合控制常规切换的缺陷，提出一种简便的基于偏差量的模糊切换方法，仿真结果表明其性能优丁一般常规切换的复合控制。     

A Switching Anti-windup Design Using Multiple Lyapunov Functions

This technical note proposes a switching anti-windup design, which aims to enlarge the domain of attraction of the closed-loop system. Multiple anti-windup gains along with an index function that orchestrates the switching among these anti-windup gains are designed based on the min function of multiple quadratic Lyapunov functions. In comparison with the design of a single anti-windup gain which maximizes a contractively invariant level set of a single quadratic Lyapunov function as a way to enlarge the domain of attraction, the use of multiple Lyapunov functions and switching in the proposed design allows the union of the level sets of the multiple Lyapunov functions, each of which is not necessarily contractively invariant, to be contractively invariant and within the domain of attraction. As a result, the resulting domain of attraction is expected to be significantly larger than the one resulting from a single anti-windup gain and a single Lyapunov function. Indeed, simulation results demonstrate such a significant improvement.      

一种基于模糊规则切换的P-FUZZY-PID控制器

针对常规P -FUZZY -PID多模控制切换时存在的问题 ,提出了一种根据偏差和偏差变化率来实现模糊切换的多模控制器。并给出了它的动态性能、抗干扰能力及鲁棒性的实验结果     

A Note on Square Rooting of Time Functions of Turing Machines

Abstract. No abstract.     

改进的Q-M逻辑函数化简方法

为进一步提高逻辑函数的化简速度,提出一种改进的Q-M逻辑函数化简方法。在迭代比较过程中设置2个权值以缩减可合并蕴涵项集合的大小,只对满足条件的蕴涵项进行合并处理,得到全部质蕴涵项。构造质蕴涵项与最小项关联图,利用启发式规则得到能蕴涵全部最小项的最少质蕴涵项集合,从而得到逻辑函数的最小覆盖,完成逻辑函数化简。实验结果表明,该算法能降低迭代次数,减少逻辑函数的化简时间。     

规则简化与模糊决策树剪枝的比较

决策树归纳学习算法是机器学习领域中解决分类问题的最有效工具之一。由于决策树算法自身的缺陷了，因此需要进行相应的简化来提高预测精度。模糊决策树算法是对决策树算法的一种改进，它更加接近人的思维方式。文章通过实验分析了模糊决策树、规则简化与模糊规则简化；模糊决策树与模糊预剪枝算法的异同，对决策树的大小、算法的训练准确率与测试准确率进行比较，分析了模糊决策树的性能，为改进该算法提供了一些有益的线索。     

EDA中函数优化方法研究

提出了EDA中易于计算机实现的逻辑函数优化方法,即在优化过程中引入多维体运算,用星积运算求素项,选择极值法求最小覆盖,并对循环函数进行处理的优化方法.大量的实验证明了该方法的正确性和易于计算机实现的有效性.因此,该方法在数字电子设计自动化中具有广泛的应用前景.     

EDA中函数优化方法研究

提出了EDA中易于计算机实现的逻辑函数优化方法 ,即在优化过程中引入多维体运算 ,用星积运算求素项 ,选择极值法求最小覆盖 ,并对循环函数进行处理的优化方法。大量的实验证明了该方法的正确性和易于计算机实现的有效性。因此 ,该方法在数字电子设计自动化中具有广泛的应用前景     

基于模糊规则切换的多模控制器

针对常规FUZZY-PID及P-FUZZY-PID多模控制切换时存在的问题，分别提出了一种根据偏差和偏差变化率来实现模糊切换的多模控制器。给出了它的动态性能、抗干扰能力及鲁棒性与常规多模控制的比较结果。     

Fuzzy Sequential Functions

Abstrat

In this paper, the sequential functions or input-output relations of fuzzy systems which are realizable by maximin machines are studied. Various problems related to these functions are examined, which include characterization and decision Problems, completion problems, extension problems, closure properties and their relations to maximin regular events. Some basic properties of maximin regular events are also presented including the extension of Kleene's theorem to the maximin case.     

网格模型化简综述

网格模型的化简对于其存储、传输、处理以及实时绘制有着重要的意义.对国内外在这一领域的工作成果进行了较为系统的介绍,并对各方面典型算法的优缺点进行了分析,最后对这一技术的发展进行了展望.     

教材管理系统实现模糊查询功能的方法研究

基于用户模糊查询的功能需求,该文作者论述了ASP.NET下运用模糊查询的设计思路,介绍了精确查询,模糊查询的实现。     

基于模糊切换的配浆过程智能控制研究

基于配浆浓度控制过程是一个突发干扰、时变以及超调量大的过程,设计了一种基于模糊切换的配浆浓度智能控制方法。该方法将模糊控制和免疫PID控制相结合,采用模糊切换方法实现了两种控制器的协调输出,兼顾了快速性、准确性和稳定性,抑制配浆过程中出现的突发干扰和超调量。实际运行结果表明,该算法提高了配浆过程中浓度控制的快速性,避免了系统超调量的影响,保证了系统的稳定性和鲁棒性,完全能满足配浆过程浓度的工艺要求。     

基于混合聚类算法的模糊函数系统辨识方法

针对传统模糊系统存在的结构难以确定和参数辨识复杂的问题,提出了一种基于混合聚类算法的模糊函数系统辨识算法.与一般的模糊函数系统相比,混合聚类算法结合模糊C均值和模糊C回归模型聚类算法的样本距离.在模型预测部分,采用高斯函数计算每个输入变量的隶属度,利用输入变量隶属度的模糊化算子得到输入向量的隶属度.应用于Box-Jenkins煤气炉数据、一个双入单出的非线性系统和Mackey-Glass混沌时间序列数据的试验结果表明,本文算法具有很好的辨识效果,从而验证了本文算法的有效性与实用性.