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.     

相关免疫函数的性质和构造

利用Walsh频谱方法给出了一个布尔函数是m阶相关免疫函数的一个充要条件, 给出了几种由已知相关免疫函数构造新的相关免疫函数的方法.     

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.     

关于具有不同基函数的标准模糊系统逼近问题的研究

在标准模糊系统的基础上建立了正规二次多项式和正规三角函数为基函数的两类新模糊系统, 进而提出了以正规三角形函数为基函数的标准模糊系统与所提出模糊系统的比较问题. 通过采用数值分析中的余项与辅助函数方法, 对上述三类模糊系统进行了误差精度的分析, 对所建立的两个新模糊系统首次给出了从单输入单输出到多输入单输出的误差界公式. 同时, 对它们的逼近误差精度进行了比较分析, 指出了三类模糊系统的优劣. 最后, 通过算例验证了上述理论结果的正确性.     

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。     

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。     

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.      

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.     

基于三角模的模糊双向联想记忆网络的性质研究

基于模糊取大算子和三角模T的模糊合成,构建了一类模糊双向自联想记忆网络Max-T FBAM.利用三角模T的伴随蕴涵算子,为这类Max-T FBAM提出了学习算法,并理论上证明了该学习算法确定的连接权矩阵是网络最大的连接权矩阵.对任意输入能使Max-T FBAM迭代一步内就进入稳定态,该类网络具有全局稳定性和可靠的存储能力.当三角模T满足利普希兹条件时,采用上述学习算法时自联想Max-T FBAM对训练模式的摄动全局拥有好的鲁棒性.最后用实验证实了理论研究,也为图像的可靠存储提供了参考.     

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.     

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。     

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.     

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.     

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.     

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。