Adaptive fuzzy rule-based classification systems

This paper proposes an adaptive method to construct a fuzzy rule-based classification system with high performance for pattern classification problems. The proposed method consists of two procedures: an error correction-based learning procedure, and an additional learning procedure. The error correction-based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance. That is, when a pattern is misclassified by a particular fuzzy rule, the grade of certainty of that rule is decreased. On the contrary, when a pattern is correctly classified, the grade of certainty is increased. Because the error correction-based learning procedure is not meaningful after all the given patterns are correctly classified, we cannot adjust a classification boundary in such a case. To acquire a more intuitively acceptable boundary, we propose an additional learning procedure. We also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules, which consists of the error correction-based learning procedure and the concept of forgetting. We can construct a compact fuzzy rule-based classification system with high performance     

A fuzzy reasoning approach for rule-based systems based on fuzzylogics

This paper presents a weighted fuzzy reasoning algorithm for rule-based systems based on weighted fuzzy logics. The proposed algorithm allows the truth values of the conditions appearing in the antecedent portions of the rules, the certainty factors of the rules, and the weights of the conditions appearing in the antecedent portions of the rules to be represented by trapezoidal fuzzy numbers. Given the fuzzy truth values of some conditions, the algorithm can perform weighted fuzzy reasoning to evaluate the fuzzy truth values of other conditions automatically.     

Performance evaluation of fuzzy rule-based classification systems obtained by multi-objective genetic algorithms

In this paper, we examine the classification performance of fuzzy if-then rules selected by a GA-based multi-objective rule selection method. This rule selection method can be applied to high-dimensional pattern classification problems with many continuous attributes by restricting the number of antecedent conditions of each candidate fuzzy if-then rule. As candidate rules, we only use fuzzy if-then rules with a small number of antecedent conditions. Thus it is easy for human users to understand each rule selected by our method. Our rule selection method has two objectives: to minimize the number of selected fuzzy if-then rules and to maximize the number of correctly classified patterns. In our multi-objective fuzzy rule selection problem, there exist several solutions (i.e., several rule sets) called “non-dominated solutions” because two conflicting objectives are considered. In this paper, we examine the performance of our GA-based rule selection method by computer simulations on a real-world pattern classification problem with many continuous attributes. First we examine the classification performance of our method for training patterns by computer simulations. Next we examine the generalization ability for test patterns. We show that a fuzzy rule-based classification system with an appropriate number of rules has high generalization ability.     

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.     

Performance evaluation of fuzzy classifier systems formultidimensional pattern classification problems

We examine the performance of a fuzzy genetics-based machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if-then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be viewed as a classifier system. In this paper, we first describe fuzzy if-then rules and fuzzy reasoning for pattern classification problems. Then we explain a genetics-based machine learning method that automatically generates fuzzy if-then rules for pattern classification problems from numerical data. Because our method uses linguistic values with fixed membership functions as antecedent fuzzy sets, a linguistic interpretation of each fuzzy if-then rule is easily obtained. The fixed membership functions also lead to a simple implementation of our method as a computer program. The simplicity of implementation and the linguistic interpretation of the generated fuzzy if-then rules are the main characteristic features of our method. The performance of our method is evaluated by computer simulations on some well-known test problems. While our method involves no tuning mechanism of membership functions, it works very well in comparison with other classification methods such as nonfuzzy machine learning techniques and neural networks.     

Hybridization of fuzzy GBML approaches for pattern classification problems

We propose a hybrid algorithm of two fuzzy genetics-based machine learning approaches (i.e., Michigan and Pittsburgh) for designing fuzzy rule-based classification systems. First, we examine the search ability of each approach to efficiently find fuzzy rule-based systems with high classification accuracy. It is clearly demonstrated that each approach has its own advantages and disadvantages. Next, we combine these two approaches into a single hybrid algorithm. Our hybrid algorithm is based on the Pittsburgh approach where a set of fuzzy rules is handled as an individual. Genetic operations for generating new fuzzy rules in the Michigan approach are utilized as a kind of heuristic mutation for partially modifying each rule set. Then, we compare our hybrid algorithm with the Michigan and Pittsburgh approaches. Experimental results show that our hybrid algorithm has higher search ability. The necessity of a heuristic specification method of antecedent fuzzy sets is also demonstrated by computational experiments on high-dimensional problems. Finally, we examine the generalization ability of fuzzy rule-based classification systems designed by our hybrid algorithm.     

An ensemble method for fuzzy rule-based classification systems

Fuzzy rule-based classification systems are very useful tools in the field of machine learning as they are able to build linguistic comprehensible models. However, these systems suffer from exponential rule explosion when the number of variables increases, degrading, therefore, the accuracy of these systems as well as their interpretability. In this article, we propose to improve the comprehensibility through a supervised learning method by automatic generation of fuzzy classification rules, designated SIFCO–PAF. Our method reduces the complexity by decreasing the number of rules and of antecedent conditions, making it thus adapted to the representation and the prediction of rather high-dimensional pattern classification problems. We perform, firstly, an ensemble methodology by combining a set of simple classification models. Subsequently, each model uses a subset of the initial attributes: In this case, we propose to regroup the attributes using linear correlation search among the training set elements. Secondly, we implement an optimal fuzzy partition thanks to supervised discretization followed by an automatic membership functions construction. The SIFCO–PAF method, analyzed experimentally on various data sets, guarantees an important reduction in the number of rules and of antecedents without deteriorating the classification rates, on the contrary accuracy is even improved.     

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.

     

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.     

Fuzzy rule interpolation based on principle membership functions and uncertainty grade functions of interval type-2 fuzzy sets

Fuzzy rule interpolation is an important research topic in sparse fuzzy rule-based systems. In this paper, we present a new method for dealing with fuzzy rule interpolation in sparse fuzzy rule-based systems based on the principle membership functions and uncertainty grade functions of interval type-2 fuzzy sets. The proposed method deals with fuzzy rule interpolation based on the principle membership functions and the uncertainty grade functions of interval type-2 fuzzy sets. It can deal with fuzzy rule interpolation with polygonal interval type-2 fuzzy sets and can handle fuzzy rule interpolation with multiple antecedent variables. We also use some examples to compare the fuzzy interpolative reasoning results of the proposed method with the ones of an existing method. The experimental result shows that the proposed method gets more reasonable results than the existing method for fuzzy rule interpolation based on interval type-2 fuzzy sets.     

Weighted Fuzzy Interpolative Reasoning Based on Weighted Increment Transformation and Weighted Ratio Transformation Techniques

In this paper, we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems. The proposed method uses weighted increment transformation and weighted ratio transformation techniques to handle weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems. It allows each variable that appears in the antecedent parts of fuzzy rules to associate with a weight between zero and one. Moreover, we also propose an algorithm that automatically tunes the optimal weights of the antecedent variables appearing in the antecedent parts of fuzzy rules. We also apply the proposed weighted fuzzy interpolative reasoning method to handle the truck backer-upper control problem. The proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system (2000), Huang and Shen's method (2008), and Chen and Ko's method (2008). The proposed method provides us with a useful way to deal with weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems.      

A NEW METHOD TO GENERATE FUZZY RULES FROM RELATIONAL DATABASE SYSTEMS FOR ESTIMATING NULL VALUES

Fuzzy decision trees can be used to generate fuzzy rules from training instances to deal with forecasting and classification problems. We propose a new method to construct fuzzy decision trees from relational database systems and to generate fuzzy rules from the constructed fuzzy decision trees for estimating null values, where the weights of attributes are used to derive the values of certainty factors of the generated fuzzy rules. We use the concept of "coefficient of determination" of the statistics to derive the weights of the attributes in relational database systems and use the normalized weights of the attributes to derive the values of certainty factors of the generated fuzzy rules. Furthermore, we also use regression equations of the statistics to construct a complete fuzzy decision tree for generating better fuzzy rules. The proposed method obtains a higher average estimated accuracy rate than the existing methods for estimating null values in relational database systems.     

Design of adaptive fuzzy model for classification problem

The main theme of this paper is to set up an adaptive fuzzy model for a new classification problem. At first, we propose a fuzzy classification model that can automatically generate the fuzzy IF-THEN rules by the features of the training database. The consequent part of the fuzzy IF-THEN rule consists of the confident value of the rule and which class the datum should belong to. Then a novel adaptive modification algorithm (AMA) is developed to tune the confident value of the fuzzy classification model. The proposed model comprises three modules, generation of the fuzzy IF-THEN rules, determination of the classification unit, and setup of the AMA. Computer simulations on the well known Wine and Iris databases have tested the performance. Simulations demonstrate that the proposed method can provide sufficiently high classification rate in comparison with other fuzzy classification models.     

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     

hGA: Hybrid genetic algorithm in fuzzy rule-based classification systems for high-dimensional problems

The aim of this work is to propose a hybrid heuristic approach (called hGA) based on genetic algorithm (GA) and integer-programming formulation (IPF) to solve high dimensional classification problems in linguistic fuzzy rule-based classification systems. In this algorithm, each chromosome represents a rule for specified class, GA is used for producing several rules for each class, and finally IPF is used for selection of rules from a pool of rules, which are obtained by GA. The proposed algorithm is experimentally evaluated by the use of non-parametric statistical tests on seventeen classification benchmark data sets. Results of the comparative study show that hGA is able to discover accurate and concise classification rules.     

Fuzzy rule base systems verification using high-level Petri nets

In this paper, we propose a Petri nets formalism for the verification of rule-based systems. Typical structural errors in a rule-based system are redundancy, inconsistency, incompleteness, and circularity. Since our verification is based on Petri nets and their incidence matrix, we need to transform rules into a Petri nets first, then derive an incidence matrix from the net. In order to let fuzzy rule-based systems detect above the structural errors, we are presenting a Petri-nets-based mechanism. This mechanism consists of three phases: rule normalization, rules transformation, and rule verification. Rules will be first normalized into Horn clauses, then transform the normalized rules into a high-level Petri net, and finally we verify these normalized rules. In addition, we are presenting our approach to simulate the truth conditions which still hold after a transition firing and negation in Petri nets for rule base modeling. In this paper, we refer to fuzzy rules as the rules with certainty factors, the degree of truth is computed in an algebraic form based on state equation which can be implemented in matrix computation in Petri nets. Therefore, the fuzzy reasoning problems can be transformed as the liner equation problems that can be solved in parallel. We have implemented a Petri nets tool to realize the mechanism presented fuzzy rules in this paper.     

The adaptive control of nonlinear systems using the Sugeno-type offuzzy logic

An adaptive fuzzy controller is synthesized from a collection of fuzzy IF-THEN rules. The parameters of the membership functions characterizing the linguistic terms in the fuzzy IF-THEN rules are changed according to some adaptive laws for the purpose of controlling a plant to track a reference trajectory. In the paper, a direct adaptive fuzzy control design method is developed for the general higher order nonlinear continuous systems. We use the Sugeno-type of the fuzzy logic system to approximate the controller. It is proved that the closed-loop system using this adaptive fuzzy controller is globally stable in the sense that all signals involved are bounded. Finally, we apply the method of direct adaptive fuzzy controllers to control an unstable system     

Use of multi-objective genetic rule selection for examining the effectiveness of inter-vehicle communication in traffic simulations

Recently, inter-vehicle communication (IVC) has been actively studied to attempt to avoid traffic congestion. In this article, we propose the idea of using fuzzy rules to examine the effectiveness of IVC. In the proposed approach, we first collect travel records (e.g., travel time, travel path, traffic volume) of vehicles with IVC from our cellular automata-based traffic simulator. Various kinds of available information for vehicles with IVC are used in the antecedent part of our fuzzy rules. The level of effectiveness of IVC is discretized into four categories (i.e., four classes) in this article. The consequent class of each fuzzy rule is one of those four classes. Next we generate a large number of fuzzy rules from the collected data. Then we select only a small number of fuzzy rules by multi-objective genetic rule selection. We use three objectives: to maximize the accuracy, to minimize the number of selected rules, and to minimize the total rule length (i.e., the total number of antecedent conditions). Our approach can find a number of nondominated fuzzy-rule-based systems with respect to their accuracy and complexity. Finally, we analyze the effectiveness of IVC using fuzzy rules in the fuzzy-rule-based systems obtained through their linguistic interpretation.     

A proposal for improving the accuracy of linguistic modeling

We propose accurate linguistic modeling, a methodology to design linguistic models that are accurate to a high degree and may be suitably interpreted. This approach is based on two main assumptions related to the interpolative reasoning developed by fuzzy rule-based systems: a small change in the structure of the linguistic model based on allowing the linguistic rule to have two consequents associated; and a different way to obtain the knowledge base based on generating a preliminary fuzzy rule set composed of a large number of rules and then selecting the subset of them best cooperating. Moreover, we introduce two variants of an automatic design method for these kinds of linguistic models based on two well-known inductive fuzzy rule generation processes and a genetic process for selecting rules. The accuracy of the proposed methods is compared with other linguistic modeling techniques with different characteristics when solving of three different applications     

A probabilistic fuzzy approach to modeling nonlinear systems

Recently, the study of incorporating probability theory and fuzzy logic has received much interest. To endow the traditional fuzzy rule-based systems (FRBs) with probabilistic features to handle randomness, this paper presents a probabilistic fuzzy neural network (ProFNN) by introducing the probability of input linguistic terms and providing linguistic meaning into the connectionist architecture. ProFNN integrates the probabilistic information of fuzzy rules into the antecedent parts and quantifies the impacts of the rules on the consequent parts using mutual subsethood, which work in conjunction with volume defuzzification in a gradient descent learning frame work. Despite the increase in the number of parameters, ProFNN provides a promising solution to deal with randomness and fuzziness in a single frame. To evaluate the performance and applicability of the proposed approach, ProFNN is carried out on various benchmarking problems and compared with other existing models with a performance better than most of them.