Mining fuzzy association rules for classification problems

The effective development of data mining techniques for the discovery of knowledge from training samples for classification problems in industrial engineering is necessary in applications, such as group technology. This paper proposes a learning algorithm, which can be viewed as a knowledge acquisition tool, to effectively discover fuzzy association rules for classification problems. The consequence part of each rule is one class label. The proposed learning algorithm consists of two phases: one to generate large fuzzy grids from training samples by fuzzy partitioning in each attribute, and the other to generate fuzzy association rules for classification problems by large fuzzy grids. The proposed learning algorithm is implemented by scanning training samples stored in a database only once and applying a sequence of Boolean operations to generate fuzzy grids and fuzzy rules; therefore, it can be easily extended to discover other types of fuzzy association rules. The simulation results from the iris data demonstrate that the proposed learning algorithm can effectively derive fuzzy association rules for classification problems.     

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.     

GENERATING FUZZY RULES FROM TRAINING DATA CONTAINING NOISE FOR HANDLING CLASSIFICATION PROBLEMS

It is obvious that one of the important tasks in a fuzzy system is to find a set of rules to deal with a specific classification problem. In recent years, many researchers focused on the research topic of generating fuzzy rules from training data for handling classification problems. In a previous paper, we presented an algorithm to construct membership functions and to generate fuzzy rules from training examples. In this paper, we extend that work to propose a new algorithm to generate fuzzy rules from training data containing noise to deal with classification problems. The proposed algorithm gets a higher classification accuracy rate and generates fewer fuzzy rules and fewer input attributes in the antecedent portions of the generated fuzzy rules.     

Evolutionary design of a fuzzy classifier from data

Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.     

Neural networks that learn from fuzzy if-then rules

An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples     

A hybrid coevolutionary algorithm for designing fuzzy classifiers

Rule learning is one of the most common tasks in knowledge discovery. In this paper, we investigate the induction of fuzzy classification rules for data mining purposes, and propose a hybrid genetic algorithm for learning approximate fuzzy rules. A novel niching method is employed to promote coevolution within the population, which enables the algorithm to discover multiple rules by means of a coevolutionary scheme in a single run. In order to improve the quality of the learned rules, a local search method was devised to perform fine-tuning on the offspring generated by genetic operators in each generation. After the GA terminates, a fuzzy classifier is built by extracting a rule set from the final population. The proposed algorithm was tested on datasets from the UCI repository, and the experimental results verify its validity in learning rule sets and comparative advantage over conventional methods.     

Learning Premises of Fuzzy Rules for Knowledge Acquisition in Classification Problems

A key issue in building fuzzy classification systems is the specification of rule conditions, which determine the structure of a knowledge base. This paper presents a new approach to automatically extract classification knowledge from numerical data by means of premise learning. A genetic algorithm is employed to search for premise structure in combination with parameters of membership functions of input fuzzy sets to yield optimal conditions of classification rules. The major advantage of our work is that a parsimonious knowledge base with a low number of rules can be achieved. The practical applicability of the proposed method is examined by computer simulations on two well-known benchmark problems of Iris Data and Cancer Data classification. Received 11 February 1999 / Revised 13 January 2001 / Accepted in revised form 13 February 2001     

Fuzzy clustering-based discretization for gene expression classification

This paper presents a novel classification approach that integrates fuzzy class association rules and support vector machines. A fuzzy discretization technique based on fuzzy c-means clustering algorithm is employed to transform the training set, particularly quantitative attributes, to a format appropriate for association rule mining. A hill-climbing procedure is adapted for automatic thresholds adjustment and fuzzy class association rules are mined accordingly. The compatibility between the generated rules and fuzzy patterns is considered to construct a set of feature vectors, which are used to generate a classifier. The reported test results show that compatibility rule-based feature vectors present a highly- qualified source of discrimination knowledge that can substantially impact the prediction power of the final classifier. In order to evaluate the applicability of the proposed method to a variety of domains, it is also utilized for the popular task of gene expression classification. Further, we show how this method provide biologists with an accurate and more understandable classifier model compared to other machine learning techniques.     

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.     

A fuzzy ID3 induction for linguistic data sets

In real life, humans communicate by means of words. Computing with words enables flexibility via fuzzy logic to reach more informative results for the classification and decision‐making. Fuzzy logic handles the imprecise information. In our paper, we propose a novel fuzzy ID3 algorithm for the classification on linguistic data set, where data can be given as linguistic variables. Linguistic variables are defined by using triangular fuzzy numbers given as LR (left‐right) fuzzy numbers. And weighted averaging based on levels (WABL) method is used as the defuzzification method for each data. Then, fuzzy c‐means algorithm is performed to handle the membership degrees for each variable given in each data set used in an experimental study. At last, the fuzzy ID3 algorithm is applied. The rules are generated, and the reasoning is done by different T‐operators. Our study is encouraged by (using) statistical analysis. In conclusion, it is seen that our algorithm proposed for linguistic data is as good as the proposed approach for numeric data. Also, it is shown that the proposed linguistic approach by using different T‐operators on linguistic data gives better results than numerical approach on some data sets.     

Fuzzy DIFACONN-miner: A novel approach for fuzzy rule extraction from neural networks

Artificial neural networks (ANNs) are mathematical models inspired from the biological nervous system. They have the ability of predicting, learning from experiences and generalizing from previous examples. An important drawback of ANNs is their very limited explanation capability, mainly due to the fact that knowledge embedded within ANNs is distributed over the activations and the connection weights. Therefore, one of the main challenges in the recent decades is to extract classification rules from ANNs. This paper presents a novel approach to extract fuzzy classification rules (FCR) from ANNs because of the fact that fuzzy rules are more interpretable and cope better with pervasive uncertainty and vagueness with respect to crisp rules. A soft computing based algorithm is developed to generate fuzzy rules based on a data mining tool (DIFACONN-miner), which was recently developed by the authors. Fuzzy DIFACONN-miner algorithm can extract fuzzy classification rules from datasets containing both categorical and continuous attributes. Experimental research on the benchmark datasets and comparisons with other fuzzy rule based classification (FRBC) algorithms has shown that the proposed algorithm yields high classification accuracies and comprehensible rule sets.     

Learning rules from incomplete training examples by rough sets

Machine learning can extract desired knowledge from existing training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete data sets. If some attribute values are unknown in a data set, it is called incomplete. Learning from incomplete data sets is usually more difficult than learning from complete data sets. In the past, the rough-set theory was widely used in dealing with data classification problems. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete data sets based on rough sets. A new learning algorithm is proposed, which can simultaneously derive rules from incomplete data sets and estimate the missing values in the learning process. Unknown values are first assumed to be any possible values and are gradually refined according to the incomplete lower and upper approximations derived from the given training examples. The examples and the approximations then interact on each other to derive certain and possible rules and to estimate appropriate unknown values. The rules derived can then serve as knowledge concerning the incomplete data set.     

AN IMPROVED KNOWLEDGE-ACQUISITION STRATEGY BASED ON GENETIC PROGRAMMING

Knowledge acquisition can deal with the task of extracting desirable or useful knowledge from data sets for a practical application. In this paper, we have modified our previous gp-based learning strategy to search for an appropriate classification tree. The proposed approach consists of three phases: knowledge creation, knowledge evolution, and knowledge output. In the creation phase, a set of classification trees are randomly generated to form an initial knowledge population. In the evolution phase, the genetic programming technique is used to generate a good classification tree. In the output phase, the final derived classification tree is transferred as a rule set, then outputted to the knowledge base to facilitate the inference of new data. One new genetic operator, separation, is designed in this proposed approach to remove contradiction, thus producing more accurate classification rules. Experimental results from the diagnosis of breast cancers also show the feasibility of the proposed algorithm.     

Fuzzy repertory table: a method for acquiring knowledge about input variables to machine learning algorithm

In this paper, we develop a technique for acquiring the finite set of attributes or variables which the expert uses in a classification problem for characterising and discriminating a set of elements. This set will constitute the schema of a training data set to which an inductive learning algorithm will be applied. The technique developed uses ideas taken from psychology, in particular from Kelly's Personal Construct Theory. While we agree that Kelly's repertory grid technique is an efficient way to do this, it has several disadvantages which we shall try to solve by using a fuzzy repertory table. With the suggested technique, we aim to obtain the set of attributes and values which the expert can use to "measure" the object type (class) on the classification problem in some way. We will also acquire some general rules to identify the expert's evident knowledge; these rules will comprise concepts belonging to their conceptual structure.     

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.     

GA-based learning for rule identification in fuzzy neural networks

Employing an effective learning process is a critical topic in designing a fuzzy neural network, especially when expert knowledge is not available. This paper presents a genetic algorithm (GA) based learning approach for a specific type of fuzzy neural network. The proposed learning approach consists of three stages. In the first stage the membership functions of both input and output variables are initialized by determining their centers and widths using a self-organizing algorithm. The second stage employs the proposed GA based learning algorithm to identify the fuzzy rules while the final stage tunes the derived structure and parameters using a back-propagation learning algorithm. The capabilities of the proposed GA-based learning approach are evaluated using a well-examined benchmark example and its effectiveness is analyzed by means of a comparative study with other approaches. The usefulness of the proposed GA-based learning approach is also illustrated in a practical case study where it is used to predict the performance of road traffic control actions. Results from the benchmarking exercise and case study effectively demonstrate the ability of the proposed three stages learning approach to identify relevant fuzzy rules from a training data set with a higher prediction accuracy than alternative approaches.     

An ACS-based framework for fuzzy data mining

Data mining is often used to find out interesting and meaningful patterns from huge databases. It may generate different kinds of knowledge such as classification rules, clusters, association rules, and among others. A lot of researches have been proposed about data mining and most of them focused on mining from binary-valued data. Fuzzy data mining was thus proposed to discover fuzzy knowledge from linguistic or quantitative data. Recently, ant colony systems (ACS) have been successfully applied to optimization problems. However, few works have been done on applying ACS to fuzzy data mining. This thesis thus attempts to propose an ACS-based framework for fuzzy data mining. In the framework, the membership functions are first encoded into binary-bits and then fed into the ACS to search for the optimal set of membership functions. The problem is then transformed into a multi-stage graph, with each route representing a possible set of membership functions. When the termination condition is reached, the best membership function set (with the highest fitness value) can then be used to mine fuzzy association rules from a database. At last, experiments are made to make a comparison with other approaches and show the performance of the proposed framework.     

Elicitation of classification rules by fuzzy data mining

Data mining techniques can be used to find potentially useful patterns from data and to ease the knowledge acquisition bottleneck in building prototype rule-based systems. Based on the partition methods presented in simple-fuzzy-partition-based method (SFPBM) proposed by Hu et al. (Comput. Ind. Eng. 43(4) (2002) 735), the aim of this paper is to propose a new fuzzy data mining technique consisting of two phases to find fuzzy if–then rules for classification problems: one to find frequent fuzzy grids by using a pre-specified simple fuzzy partition method to divide each quantitative attribute, and the other to generate fuzzy classification rules from frequent fuzzy grids. To improve the classification performance of the proposed method, we specially incorporate adaptive rules proposed by Nozaki et al. (IEEE Trans. Fuzzy Syst. 4(3) (1996) 238) into our methods to adjust the confidence of each classification rule. For classification generalization ability, the simulation results from the iris data demonstrate that the proposed method may effectively derive fuzzy classification rules from training samples.     

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 NEW METHOD TO GENERATE FUZZY RULES FROM TRAINING INSTANCES FOR HANDLING CLASSIFICATION PROBLEMS

A major task in developing a fuzzy classification system is to generate a set of fuzzy rules from training instances to deal with a specific classification problem. In recent years, many methods have been developed to generate fuzzy rules from training instances. We present a new method to generate fuzzy rules from training instances to deal with the Iris data classification problem. The proposed method can discard some useless input attributes to improve the average classification accuracy rate. It can obtain a higher average classification accuracy rate and it generates fewer fuzzy rules and fewer input fuzzy sets in the generated fuzzy rules than the existing methods.