Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno （TS） fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1） The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from controlrelevant physical models. 2） A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3） Both numerical and linguistic inputs can be accepted for predicting new outputs. The proposed techniques are demonstrated by means of two examples： a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.     

A multilevel weighted fuzzy reasoning algorithm for expert systems

The applications of fuzzy production rules (FPR) are rather limited if the relative degree of importance of each proposition in the antecedent contributing to the consequent (i.e., the weight) is ignored or assumed to be equal. Unfortunately, this is the case for many existing FPR and most existing fuzzy expert system development shells or environments offer no such functionality for users to incorporate different weights in the antecedent of FPR. This paper proposes to assign a weight parameter to each proposition in the antecedent of a FPR and a new fuzzy production rule evaluation method (FPREM) which generalizes the traditional method by taking the weight factors into consideration is devised. Furthermore, a multilevel weighted fuzzy reasoning algorithm (MLWFRA) incorporating this new FPREM, which is based on the reachability and adjacent place characteristics of a fuzzy Petri net, is developed. The MLWFRA has the advantages that i) it offers multilevel reasoning capability; ii) it allows multiple conclusions to be drawn if they exist; iii) it offers a new fuzzy production rule evaluation method; and iv) it is capable of detecting cycle rules     

A biologically inspired solution for fuzzy shortest path problems

By considering the uncertainty that exists in the edge weights of the network, fuzzy shortest path problems, as one of the derivative problems of shortest path problems, emerge from various practical applications in different areas. A path finding model, inspired by an amoeboid organism, Physarum polycephalum, has been shown as an effective approach for deterministic shortest path problems. In this paper, a biologically inspired algorithm called Fuzzy Physarum Algorithm (FPA) is proposed for fuzzy shortest path problems. FPA is developed based on the path finding model, while utilizing fuzzy arithmetic and fuzzy distance to deal with fuzzy issues. As a result, FPA can represent and handle the fuzzy shortest path problem flexibly and effectively. Distinct from many existing methods, no order relation has been assumed in the proposed FPA. Several examples, including a tourist problem, are given to illustrate the effectiveness and flexibility of the proposed method and the results are compared with existing methods.     

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.     

基于FLcom的模糊知识推理与搜索处理

基于区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLcom,研究模糊知识及其不同否定的区分与形式表示,以及模糊知识推理与搜索处理。依据FLcom的语义解释,定义模糊命题的否定算子。具体采用Zadeh算子作为模糊推理算法,给出规则路径表的定义,利用规则路径表表示模糊推理规则及搜索过程。通过一个交通事故模型,讨论该模型的模糊推理及搜索过程,给出了搜索的算法及其实现结果。     

区分3种否定的模糊命题逻辑系统及其应用

在模糊知识表示与推理中,否定信息扮演了一个重要角色.从概念层面上区分了模糊知识中存在的3 种否定关系,即矛盾否定关系、对立否定关系和中介否定关系.为了建立能够完全描述这些不同否定关系的逻辑基础,提出一种区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM.讨论了FLCOM 特有的性质与意义,给出了FLCOM 的一种语义解释,并证明了可靠性定理.为了表明FLCOM 处理实际问题的适用性,进一步研究了FLCOM在一个模糊决策实例中的应用.具体地,基于FLCOM讨论了决策规则中的模糊命题及其不同否定的区分与形式表示,给出一种确定模糊命题及其不同否定的真值及其真值范围阈值的方法,并采用模糊产生式规则讨论了实例中的模糊推理与决策.从而表明,运用FLCOM 处理具有模糊性并且存在不同否定的实际问题是有效的.     

A two-stage evolutionary process for designing TSK fuzzy rule-basedsystems

Nowadays, fuzzy rule-based systems are successfully applied to many different real-world problems. Unfortunately, relatively few well-structured methodologies exist for designing and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi-Sugeno-Kang (TSK) fuzzy rule-based systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK fuzzy rule-based systems from examples combining a generation stage based on a (mu, lambda)-evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some three-dimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdani-type fuzzy rule-based systems in the first case, and classical regression and neural modeling in the second.     

基于数值型数据的模糊规则快速挖掘方法

针对数值型数据能准确反应现实世界，但难以理解的问题，为了从数值型数据中挖掘出易于理解的知识，提出了基于数值型数据的模糊规则快速挖掘方法。该方法能从数值型数据中挖掘出一个零阶的Sugeno模糊规则，并采用一种启发式方法将这个零阶的Sugeno模糊规则的数值结论转变为两个带置信度的语言变量，并给出了规则库的存储结构。最后通过实例证明了这种快速模糊规则挖掘方法能避免复杂的数值型计算和能有效逼近非线性函数的优点．     

An intelligent search path

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) such that the sum of the weights of its constituent edges is minimized. An example is finding the quickest way to get from one location to another on a road map; In this case, the vertices represent locations and the edges represent segments of road and are weighted by the time needed to travel that segment. In this paper, a simple method to find the shortest path in a fuzzy environment is proposed. Here the edge weights of the network are considered as fuzzy numbers so that the imprecise data values can be represented. © 2010 Wiley Periodicals, Inc.     

采用新的DNA进化算法自动设计Takagi-Sugeno模糊控制器

提出一种新颖的基于DNA的进化算法(DNA-EA)来自动设计一类Trakagi-Sugeno (TS)模糊控制器.TS模糊控制器采用带有线性规则后项的TS模糊规则,连续输 入模糊集,Zadeh模糊逻辑和常用的重心反模糊器.TS模糊控制器被证明是带有可变增 益的非线性PI控制器.DNA-EA被用于自动获取TS模糊规则,并同时优化模糊规则前 项和后项中的设计参数.DNA-EA采用由生物DNA结构启发得到的DNA编码方法来编 码模糊控制器的设计参数.在DNA-EA中,引入了受微生物进化现象启发的基因转移和细 菌变异操作.另外,也引入了基于DNA遗传操作的框构变异操作.DNA编码方法非常适 合于复杂知识的表达,基于基因水平的遗传操作也很容易引入到DNA-EA中.染色体的长 度是可变的,且可插入或删除部分碱基序列.作为示例,给出了采用DNA-EA来自动设计 TS模糊控制器用于控制一类非线性系统的方法.DNA-EA能自动地构造模糊控制器.计 算机仿真结果表明,DNA-EA是有效的,且优化得到的模糊控制器是满意的.     

应急模糊网络系统最大满意度路径的选取

讨论给定限制期条件下的应急系统模糊路径问题.当边的长度为对称三角模糊数 (Symmetric Triangular Fuzzy Number)时,由于模糊数的不可比性,网络中一般不存在绝对 最短的路.为此,引入了路径满意度函数的概念,从而问题就变成:寻找一条从起点到终点的 通路,应急车辆经过此路的时间不超过限制期t的满意度最大.这样的路径选取问题实际可 转化为一个比例路径问题,尽管许多比例路径问题已被证明是NP问题,完全可以针对问题 的具体特点,运用最短路方法的变权迭代实现对该问题的精确求解.     

Knowledge representation using fuzzy Petri nets-revisited

In the paper by S. Chen et al. (see ibid., vol.2, no.3, p.311-19, 1990), the authors proposed an algorithm which determines whether there exists an antecedent-consequence relationship from a fuzzy proposition d _s to proposition d_j and if the degree of truth of proposition d_s is given, then the degree of truth of proposition d_j can be evaluated. The fuzzy reasoning algorithm proposed by S. Chen et al. (1990) was found not to be working with all types of data. We propose: (1) a modified form of the algorithm, and (2) a concept of hierarchical fuzzy Petri nets for data abstraction     

Takagi-Sugeno fuzzy modeling incorporating input variables selection

Fuzzy models, especially Takagi-Sugeno (T-S) fuzzy models, have received particular attention in the area of nonlinear modeling due to their capability to approximate any nonlinear behavior. Based only on measured data without any prior knowledge, there is no systematic way to obtain a T-S fuzzy model with a simple structure and sufficient accuracy. The main idea discussed in this paper is to reduce the complexity of T-S fuzzy models by estimating an optimal number of fuzzy rules and selecting relevant inputs as antecedent variables independently of the selection of consequent regressors. A systematic procedure is proposed here and illustrated on static and dynamical nonlinear systems.     

Knowledge Representation Using High-Level Fuzzy Petri Nets

This correspondence presents a high-level fuzzy Petri net (HLFPN) model to represent the fuzzy production rules of a knowledge-based system, where a fuzzy production rule is the one that describes the fuzzy relation between the antecedent and the consequent. The HLFPN can be used to model fuzzy IF-THEN rules and IF-THEN-ELSE rules, where the fuzzy truth values of the propositions are restricted to [0, 1]. Based on the HLFPN model, an efficient algorithm is proposed to automatically reason about imprecise and fuzzy information. In this correspondence, a novel model to represent fuzzy knowledge is developed. When compared with other related models, the HLFPN model preserves several significant advantages. Finally, main results are presented in the form of eight properties and are supported by a comparison with other existing algorithms     

A reduction approach for fuzzy rule bases of fuzzy controllers

In this paper, a new approach to reducing the number of rules in a given fuzzy rule base of a fuzzy controller is presented. The fuzzy mechanism of the fuzzy controller under consideration consists of the product-sum inference, singleton output consequents and centroid defuzzification. The output consequents in the cells of the rule table are collected and represented as an output consequent matrix. The feature of the output consequent matrix is extracted by the singular values of the matrix. The output consequent matrix is reasonably approximated with a dominant consequent matrix. Also, the elements of the dominant consequent matrix is determined to minimize the approximation error function. Then the size of the dominant consequent matrix (the size of the fuzzy rule base) is reduced through the rule combination approach. The scaling factors for the fuzzy controller with the reduced rule table are adjusted to have the control system satisfy the performance indices. The effectiveness of the proposed approach is shown using simulation and experimental results.     

A reasoning algorithm for high-level fuzzy Petri nets

We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query     

直觉模糊研究的知识结构及知识流动分析

为了全面分析直觉模糊领域的研究概况、知识结构、知识扩散路径以及活跃研究子领域,基于主路径方法,结合知识图谱工具,对中国知网(CNKI)数据库中收录的与直觉模糊研究相关的文献进行系统分析.研究结果表明:直觉模糊领域已进入成熟阶段,且2007年与2014年的研究成果受到了广泛关注;从直觉模糊领域的知识结构看,直觉模糊集合、...     

Ant Colony Optimization Incorporated With Fuzzy Q-Learning for Reinforcement Fuzzy Control

This paper proposes the design of fuzzy controllers by ant colony optimization (ACO) incorporated with fuzzy-Q learning, called ACO-FQ, with reinforcements. For a fuzzy inference system, we partition the antecedent part a priori and then list all candidate consequent actions of the rules. In ACO-FQ, the tour of an ant is regarded as a combination of consequent actions selected from every rule. Searching for the best one among all combinations is partially based on pheromone trail. We assign to each candidate in the consequent part of the rule a corresponding Q-value. Update of the Q-value is based on fuzzy-Q learning. The best combination of consequent values of a fuzzy inference system is searched according to pheromone levels and Q-values. ACO-FQ is applied to three reinforcement fuzzy control problems: (1) water bath temperature control; (2) magnetic levitation control; and (3) truck backup control. Comparisons with other reinforcement fuzzy system design methods verify the performance of ACO-FQ.     

Stability and stabilizability of fuzzy-neural-linear controlsystems

This paper discusses stability analysis of fuzzy-neural-linear (FNL) control systems which consist of combinations of fuzzy models, neural network (NN) models, and linear models. The authors consider a relation among the dynamics of NN models, those of fuzzy models and those of linear models. It is pointed out that the dynamics of linear models and NN models can be perfectly represented by Takagi-Sugeno (T-S) fuzzy models whose consequent parts are described by linear equations. In particular, the authors present a procedure for representing the dynamics of NN models via T-S fuzzy models. Next, the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of Lyapunov. The stability criteria is reduced to the problem of finding a common Lyapunov function for a set of Lyapunov inequalities. The stability conditions are employed to analyze stability of FNL control systems. Finally, stability analysis for four types of FNL control systems is demonstrated     

FWM树脂粘度测量控制系统的研究

纤维增强塑料(FRP)制品在航空航天、化工等行业应用非常广泛,但在其制造过程(如,预浸料和挤拉等生产工艺)中,纤维缠绕机械(FWM)上树脂粘度的在线测量和连续控制一直都是实际控制工程难以解决的难题。提出的FWM纤维树脂粘度控制系统采用单筒式测量法和模糊控制技术对树脂粘度进行测量控制的方案,不但结构简单、编程调试方便、能显示控制曲线,而且,能通过人机界面随时改变粘度的设定值和模糊控制器的参数,极大地改善了控制的性能,达到了预期的效果。