Using fuzzy partitions to create fuzzy systems from input-outputdata and set the initial weights in a fuzzy neural network

We create a set of fuzzy rules to model a system from input-output data by dividing the input space into a set of subspaces using fuzzy partitions. We create a fuzzy rule for each subspace as the input space is being divided. These rules are combined to produce a fuzzy rule based model from the input-output data. If more accuracy is required, we use the fuzzy rule-based model to determine the structure and set the initial weights in a fuzzy neural network. This network typically trains in a few hundred iterations. Our method is simple, easy, and reliable and it has worked well when modeling large “real world” systems     

An efficient single output fuzzy control algorithm for adaptive applications

A new single output fuzzy control algorithm which is simple and efficient is developed in the paper. Assuming standard type membership functions, a fuzzy set is characterized in this approach by that element in the fuzzy set with maximal membership. Fuzzy rules are then represented by a set of numbers. The algorithm uses a matrix representation of the rules in which the input part of the rule is used as an index, and the indexed element is the corresponding output. This is shown to allow for easy expansion of the output universe. Modification and introduction of new rules are further shown to be very simple and as a salient feature the efficiency of the algorithm is found to increase, when the number of rules increases. This new algorithm is therefore particularly useful and efficient when combined with a rule adaption mechanism. Because of simplicity and efficiency, this algorithm is very suitable for implementation even on small micro processor systems, making adaptive fuzzy control feasible for industrial applications, where a fast and nonlinear control is required.     

A review of the construction of hierarchical fuzzy systems

Fuzzy rule‐based systems are nowadays one of the most successful applications of fuzzy sets and fuzzy logic. Most applications use a flat set of fuzzy rules. However, in complex applications with a large set of variables, it is not appropriate to define the system with a flat set of rules because, among other problems, the number of rules increases exponentially with the number of variables. Hierarchical fuzzy systems are one of the alternatives presented in the literature to overcome this problem. In this article we review the latest results related with this type of fuzzy system. © 2002 Wiley Periodicals, Inc.     

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.     

Generating fuzzy rules for target tracking using a steady-stategenetic algorithm

Radar target tracking involves predicting the future trajectory of a target based on its past positions. This problem has been dealt with using trackers developed under various assumptions about statistical models of process and measurement noise and about target dynamics. Due to these assumptions, existing trackers are not very effective when executed in a stressful environment in which a target may maneuver, accelerate, or decelerate and its positions be inaccurately detected or missing completely from successive scans. To deal with target tracking in such an environment, recent efforts have developed fuzzy logic-based trackers. These have been shown to perform better as compared to traditional trackers. Unfortunately, however, their design may not be easier. For these trackers to perform effectively, a set of carefully chosen fuzzy rules are required. These rules are currently obtained from human experts through a time-consuming knowledge acquisition process of iterative interviewing, verifying, validating, and revalidating. To facilitate the knowledge acquisition process and ensure that the best possible set of rules be found, we propose to use an automatic rule generator that was developed based on the use of a genetic algorithm (GA). This genetic algorithm adopts a steady-state reproductive scheme and is referred to as the steady-state genetic algorithm (SSGA) in this paper. To generate fuzzy rules, we encode different rule sets in different chromosomes. Chromosome fitness is then determined according to a fitness function defined in terms of the number of track losses and the prediction accuracy when the set of rules it encodes is tested against training data. The rules encoded in the fittest chromosome at the end of the evolutionary process are taken to be the best possible set of fuzzy rules     

基于UKF的自适应模糊推理神经网络

如何生成最优的模糊规则数及模糊规则的自动生成和修剪是模糊神经网络训练算法研究的重点。针对这一问题,本文提出了基于UKF的自适应模糊推理神经网络(UKF-ANFIS)。首先,通过减法聚类确定UKF-ANFIS的模糊规则及其高斯隶属函数的中心和宽度参数;其次,分析了模糊神经网络的非线性动力系统表示,并用LLS和UKF分别学习线性和非线性的参数;然后,用误差下降率方法作为模糊规则修剪的策略,删除作用不大的规则;最后,通过典型的函数逼近和系统辨识实例,表明本文算法得到的模糊神经网络的结构更为紧凑,泛化性能也更佳。     

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.     

多变量模糊系统控制设计及其在并行混合电动汽车中的应用

利用矩阵半张量积方法研究了多变量模糊系统模糊逻辑控制器的设计,并得到了若干新的结果.首先给出了模糊规则新的表示形式,基于该表示形式,构造了模糊逻辑控制器的结构矩阵,将复杂的模糊推理转变成了简单的代数等式.然后当模糊控制规则不完全时,建立了最小入度控制算法;当模糊控制规则不一致时,给出了相应的处理方法.最后将得到的结果应用到并行混合电动汽车(PHEV)能量管理和控制策略的模糊控制器设计.     

Designing fuzzy inference systems from data: Aninterpretability-oriented review

Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from data. Designing a FIS from data can be decomposed into two main phases: automatic rule generation and system optimization. Rule generation leads to a basic system with a given space partitioning and the corresponding set of rules. System optimization can be done at various levels. Variable selection can be an overall selection or it can be managed rule by rule. Rule base optimization aims to select the most useful rules and to optimize rule conclusions. Space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters. Structure optimization is of a major importance: selecting variables, reducing the rule base and optimizing the number of fuzzy sets. Over the years, many methods have become available for designing FIS from data. Their efficiency is usually characterized by a numerical performance index. However, for human-computer cooperation another criterion is needed: the rule interpretability. An implicit assumption states that fuzzy rules are by nature easy to be interpreted. This could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts. The paper analyzes the main methods for automatic rule generation and structure optimization. They are grouped into several families and compared according to the rule interpretability criterion. For this purpose, three conditions for a set of rules to be interpretable are defined     

Inductive rule generation and interpretation

Abstract

The problem of knowledge acquisition has been recognized as the major bottleneck in the development of knowledge-based systems. An encouraging approach to alleviate this problem is inductive learning. Inductive learning systems accept, as input, a set of data that represent instances of the problem domain and produce, as output, the rules of the knowledge base. Each data item is described by a set of attribute values and is assigned to a unique decision class. A common characteristic of the existing inductive learning systems, is that they are empirical in nature and do not take into account the implications of the inductive rule generation process on the performance of the resulting set of rules. That performance is assessed when the rules are used to classify new unlabelled data. This paper demonstrates that the performance of a rule set is a function of the rule generation and rule interpretation processes. These two processes are interrelated and should not be considered separately. The interrelation of rule generation and rule interpretation is analysed and suggestions to improve the performance of existing inductive learning systems, are forwarded.     

AGFS: Adaptive Genetic Fuzzy System for medical data classification

A Genetic Fuzzy System (GFS) is basically a fuzzy system augmented by a learning process based on a genetic algorithm (GA). Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridize fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. The GA can be merged with Fuzzy system for different purposes like rule selection, membership function optimization, rule generation, co-efficient optimization, for data classification. Here we propose an Adaptive Genetic Fuzzy System (AGFS) for optimizing rules and membership functions for medical data classification process. The primary intension of the research is 1) Generating rules from data as well as for the optimized rules selection, adapting of genetic algorithm is done and to explain the exploration problem in genetic algorithm, introduction of new operator, called systematic addition is done, 2) Proposing a simple technique for scheming of membership function and Discretization, and 3) Designing a fitness function by allowing the frequency of occurrence of the rules in the training data. Finally, to establish the efficiency of the proposed classifier the presentation of the anticipated genetic-fuzzy classifier is evaluated with quantitative, qualitative and comparative analysis. From the outcome, AGFS obtained better accuracy when compared to the existing systems.     

Fuzzy rule interpolation based on the ratio of fuzziness of interval type-2 fuzzy sets

In recent years, some fuzzy rule interpolation methods have been presented for sparse fuzzy rule-based systems based on interval type-2 fuzzy sets. However, the existing methods have the drawbacks that they cannot guarantee the convexity of the fuzzy interpolated result and may generate the same fuzzy interpolated results with respect to different observations. Moreover, they also cannot deal with fuzzy rule interpolation with bell-shaped interval type-2 fuzzy sets. In this paper, we present a new method for fuzzy rule interpolation for sparse fuzzy rule-based systems based on the ratio of fuzziness of interval type-2 fuzzy sets. The proposed method can overcome the drawbacks of the existing methods. First, it calculates the weights of the closest fuzzy rules with respect to the observation to obtain an intermediate consequence fuzzy set. Then, it uses the ratio of fuzziness of interval type-2 fuzzy sets to infer the fuzzy interpolated result based on the intermediate consequence fuzzy set. We also use some examples to compare the fuzzy interpolated results of the proposed method with the results by the existing methods. The experimental results show that the proposed fuzzy rule interpolation method gets more reasonable results than the existing methods.     

A new method for constructing membership functions and fuzzy rulesfrom training examples

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cuts of fuzzy sets to construct the membership functions of the input variables and the output variables of fuzzy rules and to induce the fuzzy rules from the numerical training data set. Based on the proposed fuzzy learning algorithm, we also implemented a program on a Pentium PC using the MATLAB development tool to deal with the Iris data classification problem. The experimental results show that the proposed fuzzy learning algorithm has a higher average classification ratio and can generate fewer rules than the existing algorithm.     

Fuzzy rule weight modification with particle swarm optimisation

The most challenging problem in developing fuzzy rule-based classification systems is the construction of a fuzzy rule base for the target problem. In many practical applications, fuzzy sets that are of particular linguistic meanings, are often predefined by domain experts and required to be maintained in order to ensure interpretability of any subsequent inference results. However, learning fuzzy rules using fixed fuzzy quantity space without any qualification will restrict the accuracy of the resulting rules. Fortunately, adjusting the weights of fuzzy rules can help improve classification accuracy without degrading the interpretability. There have been different proposals for fuzzy rule weight tuning through the use of various heuristics with limited success. This paper proposes an alternative approach using Particle Swarm Optimisation in the search of a set of optimal rule weights, entailing high classification accuracy. Systematic experimental studies are carried out using common benchmark data sets, in comparison to popular rule based learning classifiers. The results demonstrate that the proposed approach can boost classification performance, especially when the size of the initially built rule base is relatively small, and is competitive to popular rule-based learning classifiers.     

Remarks on the cellular automaton global synchronisation problem: deterministic versus stochastic models

In the global synchronisation problem, one is asked to find a cellular automaton which has the property that every initial condition evolves into a homogeneous blinking state. We study this simple inverse problem for the case of one-dimensional systems with periodic boundary conditions. Two paradoxical observations are made: (a) despite the apparent simplicity of finding rules with good statistical results, there exist no perfect deterministic solutions to this problem, (b) if we allow the use of randomness in the local rule, constructing “perfect” stochastic solutions is easy. For the stochastic case, we give some rules for which the mean time of synchronisation varies quadratically with the number of cells and ask if this result can be improved. To explore more deeply the deterministic rules, we code our problem as a SAT problem and use SAT solvers to find rules that synchronise a large set of initial conditions (in appendix).

     

A tuned hybrid intelligent fruit fly optimization algorithm for fuzzy rule generation and classification

Fuzzy rule-based systems (FRBSs) are well-known soft computing methods commonly used to tackle classification problems characterized by uncertainties and imprecisions. We propose a hybrid intelligent fruit fly optimization algorithm (FOA) to generate and classify fuzzy rules and select the best rules in a fuzzy if–then rule system. We combine a FOA and a heuristic algorithm in a hybrid intelligent algorithm. The FOA is used to create, evaluate and update triangular fuzzy rule-based and orthogonal fuzzy rule-based systems. The heuristic algorithm is used to calculate the certainty grade of the rules. The parameters in the proposed hybrid algorithm are tuned using the Taguchi method. An experiment with 27 benchmark datasets and a tenfold cross-validation strategy is designed and carried out to compare the proposed hybrid algorithm with nine different FRBSs. The results show that the hybrid algorithm proposed in this study is significantly more accurate than the nine competing FRBSs.

     

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.     

Stabilization of unstable and unintuitive plants by fuzzy control

A heuristically derived stabilization strategy for an unstable and unintuitive plant by fuzzy control is described. It is shown that the often used classical fuzzy controller, which is both static and time invariant, is incapable of stabilizing such types of plants. However, a simple modification to the classical fuzzy controller architecture that separates the measurement and control phases, together with a hierarchical control strategy, enable the unstable and unintuitive plant to be stabilized. The fuzzy control strategy, as well as the new fuzzy controller architecture, are based on the consideration of "what a human subject would do when dealing with a physical plant which is both unstable and unintuitive". The stabilization strategy is then generalized to other mathematically similar systems. While the rules for the stabilization of the plant are heuristically defined, the membership functions associated with the rules are tuned by a simulated annealing procedure.     

A Strategy of Dynamic Reasoning in Knowledge-Based System with Fuzzy Production Rules

Fuzzy production rules have been successfully applied to represent uncertainty in a knowledge-based system. The knowledge organized as a knowledge base is static. On the other hand, a real system such as the stock market is dynamic in nature. Therefore we need a strategy to reflect the dynamic nature of a system when we make reasoning with a knowledge-based system.This paper proposes a strategy of dynamic reasoning that can be used to takes account the dynamic behavior of decision-making with the knowledge-based system consisted of fuzzy rules. A degree of match (DM) between actual input information and antecedent of a rule is represented by a value in interval [0, 1]. Weights of relative importance of attributes in a rule are obtained by the AHP (Analytic Hierarchy Process) method. Then these weights are applied as exponents for the DM, and the DMs in a rule are combined, with the Min operator, into a single DM for the rule. In this way, the importance of attributes of a rule, which can be changed from time to time, can be reflected to reasoning in knowledge-based system with fuzzy rules.With the proposed reasoning procedure, a decision maker can take his judgment on the given decision environment into a static knowledge base with fuzzy rules when he makes decision with the knowledge base. This procedure can be automated as a pre-processing system for fuzzy expert systems. Thereby the quality of decisions could be enhanced.     

AUTOMATICALLY CONSTRUCTING MEMBERSHIP FUNCTIONS AND GENERATING FUZZY RULES USING GENETIC ALGORITHMS

The most important task in designing a fuzzy classification system is to find a set of fuzzy rules from training data to deal with a specific classification problem. In recent years, many methods have been proposed to construct membership functions and generate fuzzy rules from training data for handling fuzzy classification problems. We propose a new method to generate fuzzy rules from training data by using genetic algorithms (GAs). First, we divide the training data into several clusters by using the weighted distance clustering method and generate a fuzzy rule for each cluster. Then, we use GAs to tune the membership functions of the generated fuzzy rules. The proposed method attains a higher average classification accuracy rate than the existing methods.