How good are fuzzy If-Then classifiers?

Knowledge and Information Systems

This paper presents a general framework for designing a fuzzy rule-based classifier. Structure and parameters of the classifier are evolved through a two-stage genetic search. To reduce the search space, the classifier structure is constrained by a tree created using the evolving SOM tree algorithm. Salient input variables are specific for each fuzzy rule and are found during the genetic search process. It is shown through computer simulations of four real world problems that a large number of rules and input variables can be eliminated from the model without deteriorating the classification accuracy. By contrast, the classification accuracy of unseen data is increased due to the elimination.

International Journal of Approximate Reasoning, 2013

The determination of fuzzy information granules including the estimation of their membership functions play a significant role in fuzzy system design as well as in the design of fuzzy rule based classifiers (FRBCSs). However, although linguistic terms are fundamental elements in the process of elucidating expert's knowledge, the problem of linguistic term design along with their fuzzy-set-based semantics has not been fully addressed, since termsets of attributes have not been interpreted as a formalized structure. Thus, the essential relationship between linguistic terms, as syntax, and the constructed fuzzy sets, as their quantitative semantics, or in other words, the problem of the natural semantics of terms behind the linguistic literal has not been addressed. In this paper, we introduce the problem of the design of optimal linguistic terms and propose a method of the design of FRBCSs which may incorporate with the design of linguistic terms to ensure that the presence of linguistic literals are supported not only by data but also by their natural semantics. It is shown that this problem plays a primordial role in enhancing the performance and the interpretability of the designed FRBCSs and helps striking a better balance between the generality and the specificity of the desired fuzzy rule bases for fuzzy classification problems. A series of experiments concerning 17 Machine Learning datasets is reported.

IEEE Transactions on Industrial Electronics, 1999

In this paper, various methods are introduced for improving the ability of fuzzy classifier systems to automatically generate fuzzy if-then rules for pattern classification problems with continuous attributes. First, we describe a simple fuzzy classifier system where a randomly generated initial population of fuzzy if-then rules is evolved by typical genetic operations, such as selection, crossover, and mutation. By computer simulations on a real-world pattern classification problem with many continuous attributes, we show that the search ability of such a simple fuzzy classifier system is not high. Next, we examine the search ability of a hybrid algorithm where a learning procedure of fuzzy if-then rules is combined with the fuzzy classifier system. Then, we introduce two heuristic procedures for improving the performance of the fuzzy classifier system. One is a heuristic rule generation procedure for an initial population where initial fuzzy if-then rules are directly generated from training patterns. The other is a heuristic population update procedure where new fuzzy if-then rules are generated from misclassified and rejected training patterns, as well as from existing fuzzy if-then rules by genetic operations. By computer simulations, we demonstrate that these two heuristic procedures drastically improve the search ability of the fuzzy classifier system. We also examine a variant of the fuzzy classifier system where the population size (i.e., the number of fuzzy if-then rules) varies depending on the classification performance of fuzzy if-then rules in the current population. Finally, the generalization ability of the fuzzy classifier system for test data is evaluated by computer simulations on a real-world pattern classification problem with both continuous and discrete attributes.

Automatic Control and Computer Sciences, Vol. 49, , 2015

In a fuzzy classifier, the maping “inputs–output” is described by the linguistic 〈If–then〉 rules, the antecedents in which contain the fuzzy terms “low,” “average,” “high,” and so on. To increase the correctness, the fuzzy classifier is learned by using experimental data. The problems with equal and different costs of various classification errors are discussed. A new criterion is offered for problems with undistinguishable types of errors, in addition to the two known criteria. A new one implies that the distance between the desired and real fuzzy results of classification for the cases of a wrong decision is weighted by the penalty factor. The learning criteria are generalized for problems of classification with the cost matrix. The conducted computer experiments on the wine recognition and heart disease diagnostics problems show that the best quality parameters of tuning fuzzy classifiers are achieved by a new learning criterion.

2004

When designing any type of fuzzy rule based system, considerable effort is placed in identifying the correct number of fuzzy sets and the fine tuning of the corresponding membership functions. Once a rule base has been formulated a fuzzy inference strategy must be applied in order to combine grades of membership. Considerable time and effort is spent trying to determine the number of fuzzy sets for a given system while substantially less time is invested in obtaining the most suitable inference strategy. This paper investigates a number of theoretical proven fuzzy inference strategies in order to assess the impact of these strategies on the performance of a fuzzy rule based classifier system. A fuzzy inference framework is proposed, which allows the investigation of five pure theoretical fuzzy inference operators in two real world applications. An additional two novel fuzzy-neural strategies are proposed and a comparative study is undertaken. The results show that the selection of the most suitable inference strategy for a given domain can lead to a significant improvement in performance.

Fuzzy Sets and Systems, 2007

This paper considers the automatic design of fuzzy rule-based classification systems from labeled data. The classification accuracy and interpretability of generated rules are of major importance in fuzzy classification systems. We propose a weighting function for compatibility grade of patterns that improves the performance of fuzzy classification system without degrading the interpretability of fuzzy rules. Our approach divides the covering subspace of each fuzzy rule into two subdivisions based on a threshold. Any pattern with compatibility grade above this threshold should be classified truly so the weighting function enhances their association degree. For patterns below threshold, their compatibility grades remain unchanged. The splitting threshold for each rule (i.e. the compatibility grade of a specific pattern) is found using distribution of patterns in the covering subspace of that rule. We also show that how the proposed approach is applicable when fuzzy rules have certainty grades. Experiments on some well-known data sets are used to evaluate the performance of our approach.

5th Online World Conference on Soft Computing in Industrial Applications, pp. 4-18, 2000

Data-based identification of fuzzy rule-based classi-fiers for high-dimensional problems is addressed. A crisp binary decision tree approach is proposed for the selection of the relevant features and effective initial par-titioning of the input domain. The decision tree is then transformed into a fuzzy rule-based classifier. Fuzzy classifiers have more flexible decision boundaries than decision trees and can therefore be more parsimonious. Therefore, the DT initialized fuzzy classifier is reduced in an iterative scheme by means of similarity-based rule-reduction. A genetic algorithm with a multi-objective criterion searching for both redundancy and accuracy is applied. The proposed approach is studied on an arti-ficial problem and the Wisconsin Breast Cancer classifi-cation problem.

MATEC Web of Conferences, 2019

When determining the degree of coincidence of any multi-feature obtained information, received in the form of a fuzzy vector, to a pre-established known pattern, two general steps should be followed. The first step is to eliminate the features that have little or no effect to the final results and to maintain only those that will influence the pattern recognition. This step could be defined as the classification process and is imperative for the simplification of the problem. One example of classification that could considerably reduce system costs is when using sensors distributed along an industrial process to manage information at a central location. Several methods could be used for classification, such as statistical methods, rough sets, fuzzy logic or information theory. The second step is to find out the correlation between the received fuzzy vector and the vector defining the known pattern using the previously selected features. For this part, the use of fuzzy logic is extre...

The ability of a rule-based system to represent generalisations is of great importance. Generalised rules allow more compact rule bases, scalability to higher dimensional spaces, faster inference and better linguistic interpretability. The issue of rule generalisation, and the interplay between general and specific rules in the same evolving population, has received a great deal of attention in the discrete-valued classifier system research community. The same issue does not appear to have received a similar level of attention in the case of fuzzy classifier systems. While it is true that generalised rule representations have been incorporated in a number of reported fuzzy classifier systems, often as an aside to other significant issues, this important feature has not yet been concentrated on in detail. The intention of this contribution is to raise awareness of the issue of generalisation in the fuzzy classifier system so that the issue may be brought under closer scrutiny. Early experimental results using a test-bed specifically designed to test the ability of the fuzzy classifier system to learn an optimal collection of co-existing general and specific fuzzy classifiers are described and discussed.

2009

This paper is concerned with a general framework for designing a fuzzy rule-based classifier. Structure and parameters of the classifier are evolved through a two-stage genetic search. The classifier structure is constrained by a tree created using the evolving SOM tree algorithm. Salient input variables are specific for each fuzzy rule and are found during the genetic search process. It is shown through computer simulations of four real world problems that a large number of rules and input variables can be eliminated from the model without deteriorating the classification accuracy.