Intuitionistic Fuzzy Automaton for Approximate String Matching

This paper introduces an intuitionistic fuzzy automaton model for computing the similarity between pairs of strings. The model details the possible edit operations needed to transform any input (observed) string into a target (pattern) string by providing a membership and non-membership value between them. In the end, an algorithm is given for approximate string matching and the proposed model computes the similarity and dissimilarity between the pair of strings leading to better approximation.     

最大乘积型Fuzzy文法与自动机

本文对提出的最大乘积型Ｆｕｚｚｙ文法与最大乘积型Ｆｕｚｚｙ自动机的关系作了详细讨论，得出了两个重要的结论。即：由给定的最大乘积型Ｆｕｚｚｙ正规文法可构造一个最大乘积型Ｆｕｚｚｙ自动机使得二者接受的语言集相同，反之亦然。从而达到自动识别语言的目的。     

Fuzzy local ω-systems

The natural language computing today demands for the study of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language, and some closure properties of fuzzy local ω-languages are presented. We introduce deterministic fuzzy finite automaton with different acceptance mode on fuzzy ω-languages and establish the relationship between these various classes of fuzzy ω-languages. We have defined deterministic fuzzy local automaton and also establish relationships between deterministic fuzzy local automaton, fuzzy local ω-language and Büchi fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.     

F—fuzzy演绎系统

本文建立了一种演绎系统FFCS,在该演义系统中可以处理具有模糊性的推理过程,区别与其他对模糊推理进行形式化的逻辑系统,FFCS对模糊假言推理FMP做了完全形式化的处理。     

直觉模糊变换半群

首先定义了直觉模糊变换半群的概念,给出了一种特殊的直觉模糊变换半群.其次,引入了直觉模糊变换半群上的直觉容许关系,讨论了两个直觉模糊变换半群间的关系,为直觉模糊有限自动机进一步的理论研究提供了代数方法.     

关于Fuzzy正则语言的一些性质

在定义Fuzzy正则语言,Fuzzy有理语言等的基础上,研究Fuzzy正则语言相关的一些性质,得到Fuzzy正则语言与Fuzzy有理语言间的对应关系,对Fuzzy有限状态自动机的简化具有应用价值。     

Fuzzy正则表达式与Fuzzy有限态自动机的关系

首先给出了Fuzzy正则表达式的定义,接着通过研究Fuzzy正则表达式与Fuzzy有限态自动机的关系,得到了两个重要性质,即：每一个Fuzzy正则表达式,都有一个非确定性的Fuzzy有限态自动机接受其代表的语言;每一个被确定性的Fuzzy有限态自动机接受的语言,都能被一个Fuzzy正则表达式表示．     

Dynamic analysis of a non-conservative band–wheel system with a moving boundary part 2: Numerical results

The dynamic formulations of a non-conservative band/wheel system with a moving boundary are derived in the companion paper by use of Hamilton’s principle and calculus of variation. In this paper, numerical simulations for the system are obtained in transient amplitudes of the string and positions of the moving boundary by a modified finite difference method (FDM). Since the moving boundary position may not locate exactly at a grid point for any computational time, a special technique of the FDM is proposed to approximate both the transversality condition of a moving boundary and the partial differential equation of the neighboring grid points. The effects of parameters such as radius of the wheel, tension of the string, propagation speeds of the longitudinal and transverse wave and various initial conditions on the transient responses are investigated and compared with those of the fixed boundary problem.     

On the Calculus of Limiting Subjets on Riemannian Manifolds

In this paper fuzzy calculus rules for subjets of order two on finite dimensional Riemannian manifolds are obtained. Then a second order singular subjet derived from a sequence of efficient subsets of symmetric matrices is introduced. Employing fuzzy calculus rules for subjets of order two and various qualification assumptions based on a second order singular subjet, calculus rules for limiting subjets on a finite dimensional Riemannian manifold are obtianed.     

Possibilistic linear regression analysis for fuzzy data

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming problems, the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters. This approach can be regarded as a fuzzy interval analysis in a fuzzy environment.     

Fuzzy有理语言与Fuzzy有限态自动机的关系

引入了fuzzy有理语言的概念,得到了∑+的子集可识别当且仅当有理的.从而揭示了fuzzy有理语言与fuzzy有限态自动机语言的关系.     

Directed acyclic subsequence graph—Overview

The subsequence matching problem is to decide, for given strings S and T, whether S is a subsequence of T. The string S is called the pattern and the string T the text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of the pattern. For this purpose we build an automaton that accepts all subsequences of given texts. This automaton is called the Directed Acyclic Subsequence Graph (DASG). We prove an upper bound for its number of states. Furthermore, we consider a modification of the subsequence matching problem: given a string S and a finite language L, we are to decide whether S is a subsequence of any string in L. We suppose that a finite automaton accepting L is given and present an algorithm for building the DASG for language L. We also mention applications of the DASG to some problems related to subsequences.     

模糊无限状态自动机及其收敛性

到目前为止,我们所研究的模糊或非模糊的自动机都是有限状态自动机.然而,关于无限状态自动机的定义及它的稳定性和收敛性都没有被讨论过.本文中,我们使用离散的反馈神经网络及网络输出空间划分方法,同时,在梯度更新算法中使用伪梯度方法,给出了模糊无限状态自动机收敛到模糊有限状态自动机的证明.     

A survey of fuzzy implication algebras and their axiomatization

The theory of fuzzy implication algebras was proposed by Professor Wangming Wu in 1990. The present paper reviews the following two aspects of studies on FI-algebras: concepts, properties and some subclasses of FI-algebras; axiomatization of the class of FI-algebras and some of its important subclasses. The main results are summarized in the current paper, the relationships between FI-algebras and several classes of important fuzzy algebras are discussed, such as BL-algebras, MTL-algebras, and residuated lattices, and propositional calculus systems of several special classes of FI-algebras are shown.     

The variance and covariance of fuzzy random variables and their applications

The concepts of the variance and covariance of fuzzy random variables and their properties are introduced. Examples show their computation and applications in statistical estimation of parameters when samples or prior information are fuzzy. As their further applications the correlation function and the criterions of mean-square calculus for fuzzy stochastic processes are established.     

Behavior of finite-nonstationary deterministic automata in a fuzzy environment

The paper presents a method of finding optimal control of generalized deterministic abstract automaton, the structure of which is given by an arbitrary finite graph in a fuzzy environment. The control is found in order to achieve a fuzzy goal, which is given as a fuzzy set in any fixed finite vertex of the automaton structural graph. The problem solution is divided into two stages. The first stage provides the greatest possible degree of achieving the fuzzy goal depending on the path from the initial graph vertex to the fixed one, while the second stage makes it possible to construct a set of input words that ensure the achievement of this goal on the selected path. The conclusion presents an example of the application of the proposed method for constructing a regular expression of control sequences for the given abstract finite-nonstationary deterministic automaton.     

基于知识的模糊神经网络的旋转机械故障诊断

提出了一种基于知识的模糊神经网络并用于故障诊断．首先基于粗糙集对样本数据进行初步规则获取,并计算规则的依赖度和条件覆盖度,然后根据规则数目进行模糊神经网络结构部分设计,规则的依赖度和条件覆盖度用于设定网络初始权重,而用遗产算法对神经网络输出参数进行优化．这样的模糊神经网络称为基于知识的模糊神经网络．使用该网络对旋转机械常见故障进行诊断,结果表明,和一般模糊神经网络相比,该网络具有训练时间短而诊断率高的特点．     

模糊随机桁架结构的动力特性双因子分析法

针对模糊随机桁架结构的动力特性分析,提出了一种新的模糊随机有限元方法．当结构的物理参数和几何尺寸同时具有模糊随机性时,利用模糊因子法和随机因子法建立了结构刚度矩阵和质量矩阵;从结构振动的Rayleigh商表达式出发,利用区间运算推导出结构动力特性模糊随机变量的计算表达式;之后利用随机变量的矩法和代数综合法,推导出结构特征值的数字特征的计算式．通过算例分析了模糊随机桁架结构参数的模糊随机性对其动力特性的影响．该方法的优点是能准确反映结构某一参数的模糊随机性对结构特征值及其数字特征的影响．     

Dynamic pricing model and algorithm for perishable products with fuzzy demand

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.