A Note on the Simplification of Fuzzy Switching Functions

Abstract

This note is concerned with the modification of the definition of fuzzy consensus. The modified version is used to find the set of all fuzzy prime implicants of a fuzzy switching function as defined in [1]. The fuzzy algebra used to derive these functions satisfies the set of axioms of a distributive lattice with unique identities under the operators of maximum and minimum as described in [5], [4], and [3].     

On Generalized Fuzzy Belief Functions in Infinite Spaces

Determined by a fuzzy implication operator, a general type of fuzzy belief structure and its induced dual pair of fuzzy belief and plausibility functions in infinite universes of discourse are first defined. Relationship between the belief-structure-based and the belief-space-based fuzzy Dempster-Shafer models is then established. It is shown that the lower and upper fuzzy probabilities induced by the fuzzy belief space yield a dual pair of fuzzy belief and plausibility functions. For any fuzzy belief structure, there must exist a fuzzy belief space such that the fuzzy belief and plausibility functions defined by the given fuzzy belief structure are just the lower and upper fuzzy probabilities induced by the fuzzy belief space, respectively. Essential properties of the fuzzy belief and plausibility functions are also examined. The fuzzy belief and plausibility functions are, respectively, a fuzzy monotone Choquet capacity and a fuzzy alternating Choquet capacity of infinite order.     

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.     

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。     

多重多维模糊推理算法的连续性和逼近性

针对多重、多维模糊推理情形,细致地研究了几类模糊推理算法是否满足连续性和逼近性,并进一步讨论了这几类算法对逼近误差的传播性能。把模糊推理算法看成是一个模糊集合到另一个模糊集合的映射,选用海明距离作为两模糊集的距离度量方法,证明了在模糊假言推理和模糊拒取式推理情形,几类多重多维模糊算法都拥有连续性。当多重多维模糊算法满足还原性时就具有逼近性;该模糊算法都不会放大逼近误差。结果对构建模糊控制系统和模糊专家系统时选用和分析模糊推理算法有一定的指导作用。     

Properties of the Realization of Inner Functions

 In this paper we investigate fundamental properties of state-space realizations for inner functions. We derive necessary and sufficient conditions for the inner function to have a realization such that the associated C ₀-semigroup is exponentially stable. Furthermore, we give necessary and sufficient conditions on the inner function such that the C ₀-semigroup is a group. Combining these results, we have that the C ₀-semigroup is an exponentially stable C ₀-group if and only if the inner function is the product of a constant of modulus one and a Blaschke product for which the zeros satisfy the Carleson–Newman condition and the zeros lie in a vertical strip bounded away from the imaginary axis. Date received: January 11, 1999. Date revised: May 16, 2002. RID="*" ID="*"This paper was supported by the Volkswagen Stiftung (RiP program at Oberwolfach) and by the Deutsche Forschungsgemeinschaft.     

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.     

基于模糊方法的切换系统稳定性研究

从实际出发提出切换系统进行模糊切换的必要性,给出模糊切换的关键因素即隶属度的确定方法.本文首先将切换系统转化为T-S模糊模型系统,这是一个非线性系统,根据克拉索夫斯基定理,给出判定此系统在原点小邻域内渐近稳定的条件,进而确定隶属度函数.大量的仿真结果证实,本文提出的使切换系统稳定的模糊方法是切实有效的.     

基于模糊切换策略的线性切换系统的稳定性

切换系统在运行中常受到干扰、时滞等影响,致使切换系统很难准确实施已确定的切换策略,因此系统的稳定性不能得到保证,鉴于此,本文基于模糊方法研究切换系统的稳定性问题,以增强系统的鲁棒性。将切换系统转换成T—S模糊模型,该系统具有非线性性;依据变量-梯度法,给出此系统在原点的小领域内渐近稳定的充分条件,同时获得模糊切换策略。系统仿真证实此方法简单而有效。     

随动定向战斗部模糊-单神经元PID控制

防空导弹随动战斗部在高速转动时存在干扰和大过载情况,伺服电机摩擦的产生,系统具有严重的非线性特点,现有的PID和模糊神经元自适应PID控制难以满足快速准确的控制要求,针对上述问题,提出了一种模糊-单神经元PID切换控制策略,结合了传统PID、单神经元网络和模糊控制的优点,在控制前期误差较大的时候采用模糊控制,在控制后期采用单神经元PID控制,并引入切换因子函数来减小了切换冲击.仿真结果显示,改进控制策略提高了随动系统的跟踪精度和速度,克服了非线性问题,满足了随动定向战斗部的工作要求.     

Properties of Symmetric Fitness Functions

The properties of symmetric fitness functions are investigated. We show that the search spaces obtained from symmetric functions have the zero-correlation structures between fitness and distance. It is also proven that symmetric functions induce a class of the hardest problems in terms of the epistasis variance and its variants. These analyses suggest that the existing quantitative measures cannot discriminate among symmetric functions, which reveals critical limitations of the measures. To take a closer look at the symmetric functions, additional analyses are performed from other viewpoints including additive separability and boundedness. It is shown that additive separability in a symmetric function is closely related to the symmetry of its subfunctions. This elucidates why most of the well-known symmetric fitness functions are additively inseparable. The properties of two-bounded symmetric functions are investigated and they are utilized in designing an efficient algorithm to check additive separability for the two-bounded functions. Throughout this paper, we heavily use the generalized Walsh transform over multary alphabets. Our results have an independent interest as a nontrivial application of the generalized Walsh analysis.     

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。     

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。     

On the Autoreducibility of Functions

This paper studies the notions of self-reducibility and autoreducibility. Our main result regarding length-decreasing self-reducibility is that any complexity class C\mathcal{C} that has a (logspace) complete language and is closed under polynomial-time (logspace) padding has the property that if all C\mathcal{C} -complete languages are length-decreasing (logspace) self-reducible then C í P\mathcal{C}\subseteq \mathrm {P} (C í L\mathcal {C}\subseteq \mathrm {L} ). In particular, this result applies to NL, NP and PSPACE. We also prove an equivalent of this theorem for function classes (for example, for #P). We also show that for several hard function classes, in particular for #P, it is the case that all their complete functions are deterministically autoreducible. In particular, we show the following result. Let f be a #P parsimonious function with two preimages of 0. We show that there are two FP functions h and t such that for all inputs x we have f(x)=t(x)+f(h(x)), h(x)≠x, and t(x)∈{0,1}. Our results regarding single-query autoreducibility of #P functions can be contrasted with random self-reducibility for which it is known that if a #P complete function were random self-reducible with one query then the polynomial hierarchy would collapse.     

Control of Underactuated Manipulators using Fuzzy Logic Based Switching Controller

This paper introduces a new concept for designing a fuzzy logic based switching controller in order to control underactuated manipulators. The proposed controller employs elemental controllers, which are designed in advance. Parameters of both antecedent and consequent parts of a fuzzy indexer are optimized by using evolutionary computation, which is performed off-line. Design parameters of the fuzzy indexer are encoded into chromosomes, i.e., the shapes of the Gaussian membership functions and corresponding switching indices of the consequent part are evolved to minimize the angular position errors. Such parameters are trained for different initial configurations of the manipulator and the common rule base is extracted. Then, these trained fuzzy rules can be brought into the online operations of underactuated manipulators. 2-DOF underactuated manipulator is taken into consideration so as to illustrate the design procedure. Computer simulation results show that the new methodology is effective in designing controllers for underactuated robot manipulators.     

一般输入的折线模糊神经网络对模糊函数的通用逼近

首先基于一种扩展原理和模糊算术得到一类前向模糊神经网络--折线模糊神经网络.当模糊神经网络的输入为一般模糊数,激励函数为单调连续型Sigmoidal函数时,分析网络的拓扑结构及相关性质.然后证明该折线模糊神经网络能作为模糊连续函数的通用逼近器,其等价条件是模糊函数的递增性.因此关于输入为一般模糊数的折线模糊网络是否为通用逼近器的问题得到解决,且折线模糊神经网络的应用范围将进一步扩大.     

论模糊概念的度量

模糊度和模糊相似度是模糊集合中模糊概念度量最常用的两种方法。根据模糊度定义,提出了几种实用方便的模糊度公式,并分析了文[3]中新模糊度公式的不正确性;同时根据模糊贴近度定义,提出了一种贴近度公式。这些新公式的引入,在模式识别等实际应用中起着重要的作用。     

光交换技术的研究进展

当前Internet上的数据通讯量正在高速增长，而电路由器和交换机处理数据的速度已远远落后于其在光纤上的传输速度，形成了所谓的“电子瓶颈”。全光通信网代表了新一代网络的发展趋势，最终要实现数据从源节点到目的节点的传输和交换始终在光域内进行。本文全面总结了实现全光网络的各种方案，详细介绍其工作原理、关键技术、发展现状，探讨了存在的问题，最后对未来光网络的发展做了总结与展望。     

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