Iterative Fuzzy Clustering Algorithm With Supervision to Construct Probabilistic Fuzzy Rule Base From Numerical Data

To deal with data patterns with linguistic ambiguity and with probabilistic uncertainty in a single framework, we construct an interpretable probabilistic fuzzy rule-based system that requires less human intervention and less prior knowledge than other state of the art methods. Specifically, we present a new iterative fuzzy clustering algorithm that incorporates a supervisory scheme into an unsupervised fuzzy clustering process. The learning process starts in a fully unsupervised manner using fuzzy c-means (FCM) clustering algorithm and a cluster validity criterion, and then gradually constructs meaningful fuzzy partitions over the input space. The corresponding fuzzy rules with probabilities are obtained through an iterative learning process of selecting clusters with supervisory guidance based on the notions of cluster-pureness and class-separability. The proposed algorithm is tested first with synthetic data sets and benchmark data sets from the UCI Repository of Machine Learning Database and then, with real facial expression data and TV viewing data.     

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.     

Orthogonal Fuzzy Rule-Based Systems: Selection of Optimum Rules

In this paper, the concept of orthogonal fuzzy rule-based systems is introduced. Orthogonal rules are an extension to the definition of orthogonal vectors when the vectors are vectors of membership functions in the antecedent part of rules. The number and combination of rules in a fuzzy rule-based system will be optimised by applying orthogonal rules. The number of rules, and subsequently the complexity of the fuzzy rule-based systems, are directly associated with the number of input variables and distinguishable membership functions for each individual input variable. A subset of rules can be used if it is known which subset provides closer behaviour to the case when all rules are used. Orthogonal fuzzy rule-based systems are proposed as a judgment as to whether the optimal rules are selected. The application of orthogonal fuzzy rules becomes essential when fuzzy rule-based systems containing many inputs are used. An illustrative example is presented to create a model for the solder paste printing stage of surface mount tech-nology.     

Integrated feature analysis and fuzzy rule-based systemidentification in a neuro-fuzzy paradigm

Most methods of fuzzy rule-based system identification (SI) either ignore feature analysis or do it in a separate phase. This paper proposes a novel neuro-fuzzy system that can simultaneously do feature analysis and SI in an integrated manner. It is a five-layered feed-forward network for realizing a fuzzy rule-based system. The second layer of the net is the most important one, which along with fuzzification of the input also learns a modulator function for each input feature. This enables online selection of important features by the network. The system is so designed that learning maintains the nonnegative characteristic of certainty factors of rules. The proposed network is tested on both synthetic and real data sets and the performance is found to be quite satisfactory. To get an "optimal" network architecture and to eliminate conflicting rules, nodes and links are pruned and then the structure is retrained. The pruned network retains almost the same level of performance as that of the original one.     

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.     

约束T-S模糊系统设计的模糊Lyapunov方法

通过引入模糊Lyapunov函数,研究一类执行器饱和的离散T-S模糊系统.对系统设计模糊抗积分饱和补偿器,得到系统稳定的充分条件,并扩大了系统的吸引域.这种方法避免了寻求一个满足系统所有模糊规则的公共正定矩阵P.最后,抗积分饱和补偿器增益通过迭代优化算法得到.     

Transparent decision support using statistical reasoning and fuzzy inference

A framework for the development of a decision support system (DSS) that exhibits uncommonly transparent rule-based inference logic is introduced. A DSS is constructed by marrying a statistically based fuzzy inference system (FIS) with a user interface, allowing drill-down exploration of the underlying statistical support, providing transparent access to both the rule-based inference as well as the underlying statistical basis for the rules. The FIS is constructed through a "pattern discovery" based analysis of training data. Such an analysis yields a rule base characterized by simple explanations for any rule or data division in the extracted knowledge base. The reliability of a fuzzy inference is well predicted by a confidence measure that determines the probability of a correct suggestion by examination of values produced within the inference calculation. The combination of these components provides a means of constructing decision support systems that exhibit a degree of transparency beyond that commonly observed in supervised-learning-based methods. A prototype DSS is analyzed in terms of its workflow and usability, outlining the insight derived through use of the framework. This is demonstrated by considering a simple synthetic data example and a more interesting real-world example application with the goal of characterizing patients with respect to risk of heart disease. Specific input data samples and corresponding output suggestions created by the system are presented and discussed. The means by which the suggestions made by the system may be used in a larger decision context is evaluated.     

Support vector learning mechanism for fuzzy rule-based modeling: a new approach

This paper describes a fuzzy modeling framework based on support vector machine, a rule-based framework that explicitly characterizes the representation in fuzzy inference procedure. The support vector learning mechanism provides an architecture to extract support vectors for generating fuzzy IF-THEN rules from the training data set, and a method to describe the fuzzy system in terms of kernel functions. Thus, it has the inherent advantage that the model does not have to determine the number of rules in advance, and the overall fuzzy inference system can be represented as series expansion of fuzzy basis functions. The performance of the proposed approach is compared to other fuzzy rule-based modeling methods using four data sets.     

基于模糊理论决策的双向二维PCA 步态识别算法

针对步态识别中的平均步态能量图像系数矩阵维数过高和分类较困难的特 点,提出一种基于模糊理论决策分类的双向二维主成分分析的步态识别算法。通过预处理技 术得到平均步态能量图并将得到的图像分割为多个子图像,利用双向二维主成分分析来降低 平均步态能量子图像的系数矩阵维数,加快识别速度。引入模糊理论决策的方法进行最近邻 分类器的分类。最后在CASIA 步态数据库上对所提出的算法进行实验,实验结果表明该算 法具有较好的识别性能并有较强的鲁棒性。     

模糊规则的学习及其在非线性系统建模中的应用

探讨用神经网络的学习算法及模糊推理方法为非线性系统建模的问题.给出了学 习模糊规则的新算法.这个算法首先用竞争学习为训练样本的输入空间进行聚类,然后为其 确定区域划分边界,并按样本输入区域学习模糊规则.文中对于模糊规则提出了相应的模糊 推理算法.并用算例验证了本文算法的有效性.     

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples.     

Designing high-level decision making systems based on fuzzy if–then rules for a point-to-point car racing game

In this paper, fuzzy rule-based systems are applied to a point-to-point car racing game. In the point-to-point car racing game, two car agents compete with each other for taking waypoints. There are three waypoints in the car racing field, each of which is assigned a number that indicates the order to take. The control process of car agents is modeled as a non-holonomic system where there are two input variables (acceleration and steering) for controlling the position, angle and velocity of the car agents. Fuzzy rule-based systems are used to make a high-level decision where the target waypoint to take is determined. Since a fuzzy rule-based system for the high-level decision making is generated in the manner of supervised learning, a set of training patterns should be given for the construction of the fuzzy rule-based systems. In this paper we examine two methods to obtain such a set of training patterns. We also examine two representations of input vectors for the fuzzy rule-based systems. We discuss the effect of obtained training patterns and the input representation on the performance of the fuzzy rule-based systems. After discussing and analyzing the experimental results, we present an adaptive framework of fuzzy rule-based systems. The performance of adaptive fuzzy rule-based systems is then examined based on the results of their non-adaptive version. A series of computational experiments are performed to show the learning ability of the adaptive fuzzy rule-based systems.     

Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems

In this paper, we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems, where the antecedent variables appearing in the fuzzy rules have different weights. We also present a weights-learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules for the proposed weighted fuzzy interpolative reasoning method. We also apply the proposed weighted fuzzy interpolative reasoning method and the proposed weights-learning algorithm to handle the truck backer-upper control problem. The experimental results show that the proposed fuzzy interpolative reasoning method using the optimally learned weights by the proposed weights-learning algorithm gets better truck backer-upper control results than the ones by the traditional fuzzy inference system and the existing fuzzy interpolative reasoning methods. The proposed method provides us with a useful way for fuzzy rules interpolation in sparse fuzzy rule-based systems.     

Structure identification in complete rule-based fuzzy systems

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters     

Developing a new uncertain rule-based fuzzy approach for evaluating the blast-induced backbreak

This study proposes a new uncertain rule-based fuzzy approach for the evaluation of blast-induced backbreak. The proposed approach is based on rock engineering systems (RES) updated by the fuzzy system. Additionally, a genetic algorithm (GA) and imperialist competitive algorithm (ICA) were employed for the prediction aim. The most key step in modeling of fuzzy RES is the coding of the interaction matrix. This matrix is responsible for analyzing the interrelationships among the parameters influencing the rock engineering activities. The codes of the interaction matrix are not unique; thus, probabilistic coding can be done non-deterministically, which allows the uncertainties to be considered in the RES analysis. To achieve the objective of this research, 62 blasts in Shur River dam region, located in south of Iran, were investigated and the required datasets were measured. The performance of the proposed models was then evaluated in accordance with the statistical criteria such as coefficient of determination (R²). The results signify the effectiveness of the proposed GA- and ICA-based models in the simulating process. R² of 0.963 and 0.934 obtained from ICA- and GA-based models, respectively, revealed that both models were capable of predicting the backbreak. Further, the fuzzy RES was introduced as a powerful uncertain approach to evaluate and predict the backbreak.

     

Weighted fuzzy reasoning using weighted fuzzy Petri nets

This paper presents a Weighted Fuzzy Petri Net model (WFPN) and proposes a weighted fuzzy reasoning algorithm for rule-based systems based on Weighted Fuzzy Petri Nets. The fuzzy production rules in the knowledge base of a rule-based system are modeled by Weighted Fuzzy Petri Nets, where the truth values of the propositions appearing in the fuzzy production rules and the certainty factors of the rules are represented by fuzzy numbers. Furthermore, the weights of the propositions appearing in the rules are also represented by fuzzy numbers. The proposed weighted fuzzy reasoning algorithm can allow the rule-based systems to perform fuzzy reasoning in a more flexible and more intelligent manner     

可理解模糊分类系统的分层演化学习

针对模糊系统的可理解性要求,结合微粒群算法和遗传算法各自的演化特点,采用两阶段学习策略,对模糊分类系统进行分层演化。首先利用微粒群算法优化各输入变量的语言值数目及对应的模糊集参数,形成候选规则集,再应用遗传算法选择规则,得到可理解的和精确的模糊分类系统。该方法几乎无需先验知识,可直接从实值数据获取模糊分类系统,应用典型分类问题为例说明其有效性。     

Fuzzy reasoning Petri nets

This paper presents a fuzzy reasoning Petri net (FRPN) model to represent a fuzzy production rule-based system. The issues of how to represent and reason about rules containing negative literals are addressed in the proposed PN model. The execution rules based on the model are defined formally using the operators in max-algebra. Then, a fuzzy reasoning algorithm is proposed to perform fuzzy reasoning automatically. The algorithm is consistent with the matrix equation expression method in the traditional PNs and allows one to exploit the maximum parallel reasoning potential embedded in the model. The legitimacy and feasibility of the proposed approach are proved and validated through a turbine fault diagnosis expert system.     

On-line multi-stage sorting algorithm for agriculture products

This paper presents an on-line multi-stage sorting algorithm capable of adapting to different populations. The sorting algorithm selects on-line the most appropriate classifier and feature subsets for the incoming population. The sorting algorithm includes two levels, a low level for population detection and a high level for classifier selection which incorporates feature selection. Population detection is achieved by an on-line unsupervised clustering algorithm that analyzes product variability. The classifier selection uses n fuzzy kNN classifiers, each trained with different feature combinations that function as input to a fuzzy rule-based decision system. Re-training of the n fuzzy kNN classifiers occurs when the rule based system cannot assign an existing classifier with high confidence level. Classification results for synthetic and real world databases are presented.     

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