New sufficient conditions for general linear SISO Takagi-Sugeno fuzzy systems as universal approximators

By the best approximation theory, it is first proved that the SISO （single-input single-output） linear Takagi-Sugeno （TS） fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature＇s results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.

Lower Approximation Reduction in Ordered Information System with Fuzzy Decision

Attribute reduction is one of the most important problems in rough set theory. This paper introduces the concept of lower approximation reduction in ordered information systems with fuzzy decision. Moreover, the judgment theorem and discernable matrix are obtained, in which case an approach to attribute reduction in ordered information system with fuzzy decision is constructed. As an application of lower approximation reduction, some examples are applied to examine the validity of works obtained in our works..

APPROXIMATION ANALYSES FOR FUZZY VALUED FUNCTIONS IN L_1(μ)-NORM BY REGULAR FUZZY NEURAL NETWORKS

By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.

Fuzzy inference systems with no any rule base and linearly parameter growth

A class of new fuzzy inference systems New-FISs is presented.Compared with the standard fuzzy system, New-FIS is still a universal approximator and has no fuzzy rule base and linearly parameter growth. Thus, it effectively overcomes the second "curse of dimensionality":there is an exponential growth in the number of parameters of a fuzzy system as the number of input variables,resulting in surprisingly reduced computational complexity and being especially suitable for applications,where the complexity is of the first importance with respect to the approximation accuracy.

APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD REGULAR FUZZY NEURAL NETWORKS

Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Precision control of inverter welding power sources by using T-S fuzzy systems

The functional relationship of approximation accuracy and number of fuzzy sets is used to find the rational balance point between the control accuracy and the control cost of fuzzy systems. This approach efficiently eliminates the drawback of rapid control cost increase caused by blind increase of fuzzy set number in practical engineering. The sufficient conditions for TS fuzzy systems as universal approximators are derived. A special T-S fuzzy system that satisfied these conditions is analyzed, and the simulation results show that when the number of fuzzy sets is increased moderately, the model parameters＇ training epochs can be effectually decreased while the model accuracy improved significantly. A practical welding power source controlled by a T-S fuzzy system is developed with satisfactory experimental results.

Design of Hybrid Fuzzy Neural Network for Function Approximation

In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.

On universal approximation capability of fuzzy systems

The universal approximation capability of fuzzy systems using translations and dilations of one fixed function (called basis function) as their membership functions is discussed. Such types of fuzzy systems are proved to be universal approximators under conditions that the basis function is integrable, with nonvanishing integral, and a.e. continuous. This result enlarges the family of fuzzy systems which can be universal approximators. Two simulation experiments are designed to verify the conclusion.

An Adaptive Learning Method for the Generation of Fuzzy Inference System from Data

Designing a fuzzy inference system(FIS)from data can be divided into two main phases:structure identification and parameter optimization.First,starting from a simple initial topology,the membership functions and system rules are defined as specific structures.Second,to speed up the convergence of the learning algorithm and lighten the oscillation,an improved descent method for FIS generation is developed.Furthermore, the convergence and the oscillation of the algorithm are system- atically analyzed.Third,using the information obtained from the previous phase,it can be decided in which region of the in- put space the density of fuzzy rules should be enhanced and for which variable the number of fuzzy sets that used to partition the domain must be increased.Consequently,this produces a new and more appropriate structure.Finally,the proposed method is applied to the problem of nonlinear function approximation.

Adaptive Force Control of in Web Handling Systems

Winding/unwinding system control is a very important issue to web handling machines. In this paper, a novel adaptive H∞ control strategy is developed for winding process control. A gain scheduling scheme is proposed based on a neural fuzzy approximator to improve the transient response and enhance tension control;the controller’s convergence and adaptive capability can be further improved by an efficient hybrid training algorithm. The effectiveness of the proposed adaptive H∞ control is verified by experimental tests. Test results show that the developed gain approximator can adaptively accommodate parameter variations in the system and improve the control performance.

An Improved SPSA Algorithm for System Identification Using Fuzzy Rules for Training Neural Networks

Simultaneous perturbation stochastic approximation （SPSA） belongs to the class of gradient-free optimization methods that extract gradient information from successive objective function evaluation. This paper describes an improved SPSA algorithm, which entails fuzzy adaptive gain sequences, gradient smoothing, and a step rejection procedure to enhance convergence and stability. The proposed fuzzy adaptive simultaneous perturbation approximation （FASPA） algorithm is particularly well suited to problems involving a large number of parameters such as those encountered in nonlinear system identification using neural networks （NNs）. Accordingly, a multilayer perceptron （MLP） network with popular training algorithms was used to predicate the system response. We found that an MLP trained by FASPSA had the desired accuracy that was comparable to results obtained by traditional system identification algorithms. Simulation results for typical nonlinear systems demonstrate that the proposed NN architecture trained with FASPSA yields improved system identification as measured by reduced time of convergence and a smaller identification error.

基于ANP-Fuzzy模型的高校移动图书馆服务质量评价研究

[目的/意义]针对现有移动图书馆服务质量评价模型不足,结合网络分析法提出一种新的服务质量评价体系,以期提高移动图书馆服务质量水平。[方法/过程]基于用户感知服务质量界定移动图书馆服务质量内涵,构建了环境质量、信息质量等4个准则维度以及13个二级指标的高校移动图书馆服务质量评价网络结构模型,并阐述各指标之间的相互作用关系。然后建立超矩阵对各级因素相对重要性权重进行估计,并检验了指标权重分布合理度。通过调查问卷收集数据,在信度与效度分析基础上,利用模糊综合评判法对某高校移动图书馆服务质量进行分层次综合评判。[结果/结论]信息质量和结果质量是最重要的准则维度,有用性和丰富性是最为关键的二级指标。运用ANP方法构建高校移动图书馆服务质量评价体系和模糊综合评判方法估计指标权重具有一定可行性。

泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。

边缘线性化方法构造的Fuzzy系统及其逼近性能分析

给出了基于边缘线性化方法构造的Fuzzy系统输出函数的一般表达式,揭示了该方法的插值机理,证明了由其构造的Fuzzy系统输出函数可归结为插值函数的形式,在此基础上,分析了该方法所构造的Fuzzy系统的逼近误差。仿真实验表明,边缘线性化方法构造的Fuzzy系统对非线性连续函数具有很高的逼近精度。

带Fuzzy外壳和Boole心脏的险象识别逻辑

结合新近发展起来的Fuzzy命题逻辑的思想和组合线路险象识别技术的背景 ,改造G del蕴涵算子和公式代数的赋值格 ,构造了另一种带Fuzzy外壳和Boole心脏的险象识别逻辑 ,对其进行了语义地研究 ,得到若干有趣的结果 .

Fuzzy系统的函数逼近功能及误差估计

揭示Fuzzy系统的函数逼近功能以及逼近效果的误差估计.首先,相对于不确定性系统,描述如何获得一个Fuzzy系统的思路和方法,它视为对一个不确定系统的逼近.然后指出,对于任意给定的一个不确定性系统,总能将它转化为一组Fuzzy推理规则,由此可构造一个Fuzzy系统,并且证明这样构造的Fuzzy系统能逼近给定的连续函数到指定的精度.随后,通过几个实例展示了Fuzzy系统逼近连续函数的性能和效果.

一种新的L-fuzzy粗糙集的刻画方法

远域作为分子的邻近结构,在模糊拓扑中起着重要的作用.能否把远域应用到粗糙集理论中用于刻画近似算子?我们在这方面进行了有益的尝试,得到了较好的结论.基于远域系统,我们讨论了串行的、自反的、弱传递的、弱一元的和传递的等性质,得到了很好的结论.

The Need for Fuzzy AI

Artificial intelligence(AI) is once again a topic of huge interest for computer scientists around the world. Whilst advances in the capability of machines are being made all around the world at an incredible rate, there is also increasing focus on the need for computerised systems to be able to explain their decisions, at least to some degree. It is also clear that data and knowledge in the real world are characterised by uncertainty.Fuzzy systems can provide decision support, which both handle uncertainty and have explicit representations of uncertain knowledge and inference processes. However, it is not yet clear how any decision support systems, including those featuring fuzzy methods, should be evaluated as to whether their use is permitted.This paper presents a conceptual framework of indistinguishability as the key component of the evaluation of computerised decision support systems. Case studies are presented in which it has been clearly demonstrated that human expert performance is less than perfect, together with techniques that may enable fuzzy systems to emulate human-level performance including variability.In conclusion, this paper argues for the need for "fuzzy AI" in two senses:(i) the need for fuzzy methodologies(in the technical sense of Zadeh's fuzzy sets and systems) as knowledge-based systems to represent and reason with uncertainty; and(ii) the need for fuzziness(in the non-technical sense) with an acceptance of imperfect performance in evaluating AI systems.