Checking the coherence and redundancy of fuzzy knowledge bases

Checking the coherence of a set of rules is an important step in knowledge base validation. Coherence is also needed in the field of fuzzy systems. Indeed, rules are often used regardless of their semantics, and it sometimes leads to sets of rules that make no sense. Avoiding redundancy is also of interest in real-time systems for which the inference engine is time consuming. A knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base. We more particularly consider knowledge bases composed of parallel fuzzy rules. Then, coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted (i.e., any value for these variables is possible) or, at least, not more restrictive than integrity constraints. Fuzzy rule representations can be implication-based or conjunction-based; we show that only implication-based models may lead to coherence problems. However, unlike conjunction-based models, they allow to design coherence checking processes. Some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules. The problem of redundancy, which is also of interest for fuzzy knowledge bases validation, is addressed for these two kinds of rules     

Mining the fuzzy control rules of aeration in a Submerged Biofilm Wastewater Treatment Process

This paper presents a special rule base extraction analysis for optimal design of an integrated neural-fuzzy process controller using an “impact assessment approach.” It sheds light on how to avoid some unreasonable fuzzy control rules by screening inappropriate fuzzy operators and reducing over fitting issues simultaneously when tuning parameter values for these prescribed fuzzy control rules. To mitigate the design efforts, the self-learning ability embedded in the neural networks model was emphasized for improving the rule extraction performance. An aeration unit in an Aerated Submerged Biofilm Wastewater Treatment Process (ASBWTP) was picked up to support the derivation of a solid fuzzy control rule base. Four different fuzzy operators were compared against one other in terms of their actual performance of automated knowledge acquisition in the system based on a partial or full rule base prescribed. Research findings suggest that using bounded difference fuzzy operator (O_b) in connection with back propagation neural networks (BPN) algorithm would be the best choice to build up this feedforward fuzzy controller design.     

Rule extraction by fuzzy modeling algorithm for fuzzy logic control of cisatracurium as a neuromuscular block

This paper provides two rule bases to control administration of cisatracurium, a non-depolarizing neuromuscular blocking agent. One rule base is extracted from the objective approach of fuzzy modeling algorithm (FMA), and the other is from the subjective approach of experts’ clinical experience. First, we established the data-acquisition system to record the manual neuromuscular block control during surgery. After collecting 15 patients data control by cisatracurium, we extracted six rules from these data via FMA. Another rule base also had six rules from experts with clinical anesthesia experience. Each rule-base was combined with three rules regarding the safety of the fuzzy controller. To compare their performance through simulations, we used the patient model established by our previous study which is a combination model consisting of a three-compartment mathematical model based on pharmacokinetics, and the Hill equation based on pharmacodynamics. In order to test the differences between these two rule-bases, the simulation used four disturbances: the different set points, the control interval strategy, the tolerance of noise effect, and the tolerance of delay time effect. The simulation shows that the FMA could successfully extract the fuzzy rules from the clinical data, and its control error is smaller than expert rules for different set point tests. However, the control error is increased and becomes worse when the set points are raised, which means that these two rule-bases are not appropriate to control the higher set points (i.e. T1% of 40 or higher). The t-test also shows that these two rule-bases performance of different set points have significant differences (p<0.05). Moreover, the results for control interval tests show that strategy has a significant influence, especially in reducing the standard deviation of control error. However, in simulations, these two rule-bases are not affected by noise disturbance, and the delay time affects only the overshoot for these two rule-bases.     

模糊粗糙集测度的分析分层建模及应急演练控制应用

针对应急救援演练控制的复杂性和难以量化问题,为实现多人参演系统的有效控制,基于分析分层过程法(analytic hierarchy process,AHP),建立一种模糊粗糙集知识测度的综合建模方法.首先,分析模糊粗糙集各类知识测度相关概念、相互联系和各自特点,通过AHP方法,建立模糊规则的分层度量模型并给出了对比矩阵的构造示例,对模糊规则进行更加精细的度量.其次,在分析应急演练知识构成的基础上,提出预案知识提取和模糊关系粗糙集的构建方法;设计了演练过程控制流程和基于本文知识综合测度方法形成的核心控制流程;通过对规则重要性排序,提高规则判别精度,提供规则选择的手段和一种规则冲突消解方法.最终,通过一个简单案例,验证了本文所提的研究工作的可行性.     

Linguistic fuzzy model identification based on PSO with different length of particles

To generate the structure and parameters of fuzzy rule base automatically, a particle swarm optimization algorithm with different length of particles (DLPPSO) is proposed in the paper. The main finding of the proposed approach is that the structure and parameters of a fuzzy rule base can be generated automatically by the proposed PSO. In this method, the best fitness (f_gbest) and the number (N_gbest) of active rules of the best particle in current generation, the best fitness (f_pbesti) which ith particle has achieved so far and the number (N_pbesti) of active rules of it when the best position emerged are utilized to determine the active rules of ith particle in each generation. To increase the diversity of structure, mutation operator is used to change the number of active rules for particles. Compared with some other PSOs with different length of particles, the algorithm has good adaptive performance. To indicate the effectiveness of the give algorithm, a nonlinear function and two time series are used in the simulation experiments. Simulation results demonstrate that the proposed method can approximate the nonlinear function and forecast the time series efficiently.     

Molecular Verification of Rule-Based Systems Based on DNA Computation

Various graphic techniques have been developed to analyze structural errors in rule-based systems that utilize inference (propositional) logic rules. Four typical errors in rule-based systems are: redundancy (numerous rule sets resulting in the same conclusion); circularity (a rule leading back to itself); incompleteness (deadends or a rule set conclusion leading to unreachable goals); and inconsistency (rules conflicting with each other). This study presents a new DNA-based computing algorithm mainly based upon Adleman's DNA operations. It can be used to detect such errors. There are three phases to this molecular solution: rule-to-DNA transformation design, solution space generation, and rule verification. We first encode individual rules using relatively short DNA strands, and then generate all possible rule paths by the directed joining of such short strands to form longer strands. We then conduct the verification algorithm to detect errors. The potential of applying this proposed DNA computation algorithm to rule verification is promising given the operational time complexity of O(n*q), in which n denotes the number of fact clauses in the rule base and q is the number of rules with longest inference chain.     

一种不确定性条件下的自适应知识学习方法

通过研究决策表和决策规则的不确定性，分析了由不分明关系划分的粒度引起的规则不确定性的两个方面，即不一致性和随机性，建立基于信息熵和粗糙集表示的不确定性信息度量的方法．利用该方法计算决策表局部最小确定性，并以此为阈值来控制规则集生成的数量，避免不必要的冗余规则的生成．同时结合Skowron的缺省规则获取算法，实现了没有领域先验知识条件下的不确定知识的自适应学习过程．试验结果表明．阈值的选取是合理的，在保持较高的决策正确率的同时，有效地控制了规则集的生成．     

MULTITUNING FUZZY CONTROL SYSTEMS DESIGN

A multituning fuzzy control system structure that involves two simple, but effective tuning mechanisms, is proposed: one is called fuzzy control rule tuning mechanism (FCRTM); the other is called dynamic scalar tuning mechanism (DSTM). In FCRTM, it is used to generate the necessary control rules with a center extension method. In DSTM, it contains three fuzzy IF-THEN rules for determining the appropriate scaling factors for the fuzzy control system. In this paper, a method based on the genetic algorithm (GA) is proposed to simultaneously choose the appropriate parameters in FCRTM and DSTM. That is, the proposed GA-based method can automatically generate the required rule base of fuzzy controller and efficiently determine the appropriate map for building the dynamic scalars of fuzzy controller. A multiobjective fitness function is proposed to determine an appropriate parameter set such that not only the selected fuzzy control structure has fewer fuzzy rules, but also the controlled system has a good control performance. Finally, an inverted pendulum control problem is given to illustrate the effectiveness of the proposed control scheme.     

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.     

Position tracking of a 3-PSP parallel robot using dynamic growing interval type-2 fuzzy neural control

Parallel robots have complicated structures as well as complex dynamic and kinematic equations, rendering model-based control approaches as ineffective due to their high computational cost and low accuracy. Here, we propose a model-free dynamic-growing control architecture for parallel robots that combines the merits of self-organizing systems with those of interval type-2 fuzzy neural systems. The proposed approach is then applied experimentally to position control of a 3-PSP (Prismatic–Spherical–Prismatic) parallel robot. The proposed rule-base construction is different from most conventional self-organizing approaches by omitting the node pruning process while adding nodes more conservatively. This helps preserve valuable historical rules for when they are needed. The use of interval type-2 fuzzy logic structure also better enables coping with uncertainties in parameters, dynamics of the robot model and uncertainties in rule space. Finally, the adaptation structure allows learning and further adapts the rule base to changing environment. Multiple simulation and experimental studies confirm that the proposed approach leads to fewer rules, lower computational cost and higher accuracy when compared with two competing type-1 and type-2 fuzzy neural controllers.     

SIGNIFICANT FUZZY RULES EXTRACTION BY AN SVD–QR-BASED APPROACH

ABSTRACT

In this article, an SVD–QR-based approach is proposed to extract the important fuzzy rules from a rule base with several fuzzy rule tables to design an appropriate fuzzy system directly from some input-output data of the identified system. A fuzzy system with fuzzy rule tables is defined to approach the input-output pairs of an identified system. In the rule base of the defined fuzzy system, each fuzzy rule table corresponds to a partition of an input space. In order to extract the important fuzzy rules from the rule base of the defined fuzzy system, a firing strength matrix determined by the membership functions of the premise fuzzy sets is constructed. According to the firing strength matrix, the number of important fuzzy rules is determined by the Singular Value Decomposition SVD, and the important fuzzy rules are selected by the SVD–QR-based method. Consequently, a reconstructed fuzzy rule base composed of significant fuzzy rules is determined by the firing strength matrix. Furthermore, the recursive least-squares method is applied to determine the consequent part of the reconstructed fuzzy system according to the gathered input-output data so that a fine fuzzy system is determined by the proposed method. Finally, three nonlinear systems illustrate the efficiency of the proposed method.     

模糊控制规则优化方法研究

模糊控制规则的选择是模糊控制器设计的关键问题之一,在现有应用遗传算法优化模糊控制规则的方法进行研究的基础上,以模糊控制规则的完整性和一致性为出发点,提出了一种用遗传算法来优化模糊控制规则的改进算法,具体给出了遗传算法设计中的各种函数和算子的确定,并将优化过的规则用于设计模糊控制器,进行仿真研究,取得了令人满意的效果。     

Using memory and fuzzy rules in a co-operative multi-thread strategy for optimization

In this article, we analyze a co-operative multi-thread search-based optimization strategy, where each solver thread represents a different optimization algorithm (or the same one with different settings), and they are all controlled by a centralized co-ordinator. We also propose the use of memory to keep track of both the state of the individual threads and the obtained solutions. Based on this memory, a very simple fuzzy rule base is used to control the system behavior.We also present the results of three computational experiments. The first of these checks the strategy by comparing it with an independent search strategy and a sequential algorithm, and the superiority of the co-operative scheme is confirmed. The second analyzes how definition of the threads affects the quality of the results, and the importance of there being a balanced set between intensification and diversification is corroborated. The third explores the use of memory with two different fuzzy rules, and the results indicate that the best combination is to use memory together with two rules (solver dependent and solver independent ones) (although this combination should not be activated at the beginning of the search in order to avoid premature convergence).     

Machine learning approach to model sport training

The aim of this study was to use a machine learning approach combining fuzzy modeling with an immune algorithm to model sport training, in particular swimming. A proposed algorithm mines the available data and delivers the results in a form of a set of fuzzy rules “IF (fuzzy conditions) THEN (class)”. Fuzzy logic is a powerful method to cope with continuous data, to overcome problem of overlapping class definitions, and to improve the rule comprehensibility. Sport training is modeled at the level of microcycle and training unit by 12 independent attributes. The data was collected in two months (February-March 2008), among swimmers from swimming sections in Wroc?aw, Poland. The swimmers had minimum of 7 years of training and reached the II class level in swimming classification from 2005 to 2008. The goal of the performed experiments was to find the rules answering the question - how does the training unit influence swimmer’s feelings while being in water the next day? The fuzzy rules were inferred for two different scales of the class to be predicted. The effectiveness of the learned set of rules reached 68.66%. The performance, in terms of classification accuracy, of the proposed approach was compared with traditional classifier schemes. The accuracy of the result of compared methods is significantly lower than the accuracy of fuzzy rules obtained by a method presented in this study (paired t-test, P < 0.05).     

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

The paper presents a multi-objective genetic approach to design interpretability-oriented fuzzy rule-based classifiers from data. The proposed approach allows us to obtain systems with various levels of compromise between their accuracy and interpretability. During the learning process, parameters of the membership functions, as well as the structure of the classifier's fuzzy rule base (i.e., the number of rules, the number of rule antecedents, etc.) evolve simultaneously using a Pittsburgh-type genetic approach. Since there is no particular coding of fuzzy rule structures in a chromosome (it reduces computational complexity of the algorithm), original crossover and mutation operators, as well as chromosome-repairing technique to directly transform the rules are also proposed. To evaluate both the accuracy and interpretability of the system, two measures are used. The first one – an accuracy measure – is based on the root mean square error of the system's response. The second one – an interpretability measure – is based on the arithmetic mean of three components: (a) the average length of rules (the average number of antecedents used in the rules), (b) the number of active fuzzy sets and (c) the number of active inputs of the system (an active fuzzy set or input means a set or input used by at least one fuzzy rule). Both measures are used as objectives in multi-objective (2-objective in our case) genetic optimization approaches such as well-known SPEA2 and NSGA-II algorithms. Moreover, for the purpose of comparison with several alternative approaches, the experiments are carried out both considering the so-called strong fuzzy partitions (SFPs) of attribute domains and without them. SFPs provide more semantically meaningful solutions, usually at the expense of their accuracy. The operation of the proposed technique in various classification problems is tested with the use of 20 benchmark data sets and compared to 11 alternative classification techniques. The experiments show that the proposed approach generates classifiers of significantly improved interpretability, while still characterized by competitive accuracy.     

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi–Sugeno–Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.      

Using Rule Quality Measures for Rule Base Refinement in Knowledge-Based Predictive Maintenance Systems

Abstract

As today’s manufacturing domain is becoming more and more knowledge-intensive, knowledge-based systems (KBS) are widely applied in the predictive maintenance domain to detect and predict anomalies in machines and machine components. Within a KBS, decision rules are a comprehensive and interpretable tool for classification and knowledge discovery from data. However, when the decision rules incorporated in a KBS are extracted from heterogeneous sources, they may suffer from several rule quality issues, which weakens the performance of a KBS. To address this issue, in this paper, we propose a rule base refinement approach with considering rule quality measures. The proposed approach is based on a rule integration method for integrating the expert rules and the rules obtained from data mining. Within the integration process, rule accuracy, coverage, redundancy, conflict, and subsumption are the quality measures that we use to refine the rule base. A case study on a real-world data set shows the approach in detail.     

Texture segmentation by frequency-sensitive elliptical competitive learning

In this paper, a new learning algorithm is proposed with the purpose of texture segmentation. The algorithm is a competitive clustering scheme with two specific features: elliptical clustering is accomplished by incorporating the Mahalanobis distance measure into the learning rules and under-utilization of smaller clusters is avoided by incorporating a frequency-sensitive term. In the paper, an efficient learning rule that incorporates these features is elaborated. In the experimental section, several experiments demonstrate the usefulness of the proposed technique for the segmentation of textured images. On the compositions of textured images, Gabor filters were applied to generate texture features. The segmentation performance is compared to k-means clustering with and without the use of the Mahalanobis distance and to the ordinary competitive learning scheme. It is demonstrated that the proposed algorithm outperforms the others. A fuzzy version of the technique is introduced, and experimentally compared with fuzzy versions of the k-means and competitive clustering algorithms. The same conclusions as for the hard clustering case hold.