Ken Nozaki

Selecting fuzzy if-then rules for classification problems using genetic algorithms

This paper proposes a genetic-algorithm-based method for selecting a small number of significant fuzzy if-then rules to construct a compact fuzzy classification system with high classification power. The rule selection problem is formulated as a combinatorial optimization problem with two objectives: to maximize the number of correctly classified patterns and to minimize the number of fuzzy if-then rules. Genetic algorithms are applied to this problem. A set of fuzzy if-then rules is coded into a string and treated as an individual in genetic algorithms. The fitness of each individual is specified by the two objectives in the combinatorial optimization problem. The performance of the proposed method for training data and test data is examined by computer simulations on the iris data of Fisher. >

Distributed representation of fuzzy rules and its application to pattern classification

Abstract This paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems. Distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space. This means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference. In order to apply distributed representation of fuzzy rules to pattern classification problems, we first propose an algorithm to generate fuzzy rules from numerical data. Next we propose a fuzzy inference method using the generated fuzzy rules. The classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation.

A simple but powerful heuristic method for generating fuzzy rules from numerical data

Abstract In this paper, we propose a simple but powerful heuristic method for automatically generating fuzzy if-then rules from numerical data. Fuzzy if-then rules with nonfuzzy singletons (i.e., real numbers) in the consequent parts are generated by the proposed heuristic method. The main advantage of the proposed heuristic method is its simplicity, i.e., it involves neither time-consuming iterative learning procedures nor complicated rule generation mechanisms. We also suggest a linguistic representation method for deriving linguistic rules from fuzzy if-then rules with consequent real numbers. The proposed linguistic approximation method consists of two linguistic rule tables, which can realize exactly the same nonlinear mapping as an original system based on fuzzy if-then rules with consequent real numbers. Using computer simulations on rice taste data, we demonstrate the high performance of the proposed heuristic method and illustrate the proposed linguistic representation method.

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.

Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms

This paper proposes a genetic-algorithm-based approach to the construction of fuzzy classification systems with rectangular fuzzy rules. In the proposed approach, compact fuzzy classification systems are automatically constructed from numerical data by selecting a small number of significant fuzzy rules using genetic algorithms. Since significant fuzzy rules are selected and unnecessary fuzzy rules are removed, the proposed approach can be viewed as a knowledge acquisition tool for classification problems. In this paper, we first describe a generation method of rectangular fuzzy rules from numerical data for classification problems. We next formulate a rule selection problem for constructing a compact fuzzy classification system as a combinatorial optimization problem with two objectives: to minimize the number of selected fuzzy rules and to maximize the number of correctly classified patterns. We then show how genetic algorithms are applied to the rule selection problem. Last, we illustrate the proposed approach by computer simulations on numerical examples and the iris data of Fisher.

Efficient fuzzy partition of pattern space for classification problems

Abstract This paper proposes an efficient fuzzy partition method of a pattern space for classification problems. The proposed method is based on the sequential subdivision of fuzzy subspaces and the generated fuzzy subspaces have different sizes. In the proposed method, first an n -dimensional pattern space is divided into 2 n fuzzy subspaces with the same size. Next one of the fuzzy subspaces is selected and subdivided into 2 n fuzzy subspaces. This procedure is iterated until a stopping condition is satisfied. Some criteria for selecting a fuzzy subspace to be subdivided are proposed and compared with each other by computer simulations. The proposed method is also compared with other fuzzy classification methods.

Empirical study on learning in fuzzy systems by rice taste analysis

Abstract The aim of this paper is to examine the ability of trainable fuzzy systems as approximators of non-linear mappings by computer simulations on real-life data. Fuzzy if-then rules with non-fuzzy singletons in the consequent part are adjusted by a gradient descent method in fuzzy systems. After examining the ability of fuzzy systems for numerical examples, we apply them to the modelling of the relation among six factors in the sensory test on rice taste. By computer simulations based on a random subsampling technique, it is shown that the performance of fuzzy systems is comparable to that of neural networks. It is also shown that pre-specified conditions such as a fuzzy partition, initial fuzzy if-then rules and the number of iterations have a significant effect on the performance of trained fuzzy systems.

Pattern classification by distributed representation of fuzzy rules

The authors introduce the concept of distributed representation of fuzzy rules and apply it to classification problems. Distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space. This means that many fuzzy rule tables are simultaneously employed, corresponding to different fuzzy partitions in fuzzy inference. To apply distributed representation of fuzzy rules to pattern classification problems, the authors first propose an algorithm to generate fuzzy rules from numerical data. Next they propose a fuzzy inference method using the generated fuzzy rules. The classification power of distributed representation was compared with that of ordinary fuzzy rules which can be viewed as a local representation.<<ETX>>

Trainable fuzzy classification systems based on fuzzy if-then rules

This paper proposes a learning method of fuzzy classification systems based on fuzzy if-then rules for subsequently modifying the grade of certainty of each fuzzy if-then rule by an error-correction learning rule. To illustrate the proposed method, we apply it to a two-class classification problem in a two-dimensional pattern space. To evaluate the performance of the proposed method, we also apply it to the iris data of Fisher. Since the learning by the proposed method is stopped when all training patterns are correctly classified, we also suggest an additional learning method that is not based on the error-correction learning rule.<<ETX>>

Acquisition of fuzzy classification knowledge using genetic algorithms

This paper proposes a genetic-algorithm-based approach to the construction of fuzzy classification systems with rectangular fuzzy rules. In the proposed approach, compact fuzzy classification systems are automatically constructed from numerical data by selecting a small number of significant fuzzy rules using genetic algorithms. Since significant fuzzy rules are selected and unnecessary fuzzy rules are removed, the proposed approach can be viewed as a knowledge acquisition tool for classification problems. In this paper, first we describe a generation method of rectangular fuzzy rules from numerical data for classification problems. Next, we formulate a rule selection problem for constructing a compact fuzzy classification system as a combinatorial optimization problem. Then we show how genetic algorithms are applied to the rule selection problem.<<ETX>>