Juan Luis Castro

Fuzzy logic controllers are universal approximators

In this paper, we consider a fundamental theoretical question on why does fuzzy control have such a good performance for a wide variety of practical problems. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and for each fixed type of membership function belonging to a wide class of membership functions, the fuzzy logic control systems using these two and any method of defuzzification are capable of approximating any real continuous function on a compact set to arbitrary accuracy. On the other hand, this result can be viewed as an existence theorem of an optimal fuzzy logic control system for a wide variety of problems. >

Are artificial neural networks black boxes

Artificial neural networks are efficient computing models which have shown their strengths in solving hard problems in artificial intelligence. They have also been shown to be universal approximators. Notwithstanding, one of the major criticisms is their being black boxes, since no satisfactory explanation of their behavior has been offered. In this paper, we provide such an interpretation of neural networks so that they will no longer be seen as black boxes. This is stated after establishing the equality between a certain class of neural nets and fuzzy rule-based systems. This interpretation is built with fuzzy rules using a new fuzzy logic operator which is defined after introducing the concept of f-duality. In addition, this interpretation offers an automated knowledge acquisition procedure.

Fuzzy systems with defuzzification are universal approximators

In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system capable of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems.

Interpretation of artificial neural networks by means of fuzzy rules

This paper presents an extension of the method presented by Benitez et al (1997) for extracting fuzzy rules from an artificial neural network (ANN) that express exactly its behavior. The extraction process provides an interpretation of the ANN in terms of fuzzy rules. The fuzzy rules presented are in accordance with the domain of the input variables. These rules use a new operator in the antecedent. The properties and intuitive meaning of this operator are studied. Next, the role of the biases in the fuzzy rule-based systems is analyzed. Several examples are presented to comment on the obtained fuzzy rule-based systems. Finally, the interpretation of ANNs with two or more hidden layers is also studied.

Learning maximal structure rules in fuzzy logic for knowledge acquisition in expert systems

The aim of this article is to present a new approach to machine learning (precisely in classification problems) in which the use of fuzzy logic has been taken into account. We intend to show that fuzzy logic introduces new elements in the identification process, mainly due to the facility to manage imprecise information. An inductive algorithm generating a set of fuzzy rules identifying the system will be achieved. The maximal structure of a fuzzy rule will be found using this algorithm.

Consistency measures for feature selection

The use of feature selection can improve accuracy, efficiency, applicability and understandability of a learning process. For this reason, many methods of automatic feature selection have been developed. Some of these methods are based on the search of the features that allows the data set to be considered consistent. In a search problem we usually evaluate the search states, in the case of feature selection we measure the possible feature sets. This paper reviews the state of the art of consistency based feature selection methods, identifying the measures used for feature sets. An in-deep study of these measures is conducted, including the definition of a new measure necessary for completeness. After that, we perform an empirical evaluation of the measures comparing them with the highly reputed wrapper approach. Consistency measures achieve similar results to those of the wrapper approach with much better efficiency.

Extraction of fuzzy rules from support vector machines

The relationship between support vector machines (SVMs) and Takagi-Sugeno-Kang (TSK) fuzzy systems is shown. An exact representation of SVMs as TSK fuzzy systems is given for every used kernel function. Restricted methods to extract rules from SVMs have been previously published. Their limitations are surpassed with the presented extraction method. The behavior of SVMs is explained by means of fuzzy logic and the interpretability of the system is improved by introducing the @l-fuzzy rule-based system (@l-FRBS). The @l-FRBS exactly approximates the SVMs decision boundary and its rules and membership functions are very simple, aggregating the antecedents with uninorms as compensation operators. The rules of the @l-FRBS are limited to two and the number of fuzzy propositions in each rule only depends on the cardinality of the set of support vectors. For that reason, the @l-FRBS overcomes the course of dimensionality and problems with high-dimensional data sets are easily solved with the @l-FRBS.

Use of a fuzzy machine learning technique in the knowledge acquisition process

Acquiring the knowledge to support an expert system is one of the key activities in knowledge engineering. Knowledge acquisition (KA) is closely related to research in the machine learning field. Any machine learning acquires some knowledge, but not enough knowledge for building expert systems. The aim of this article is to present a new approach to machine learning which helps to acquire knowledge when building expert systems. This technique will acquire the more general knowledge that should be used for extending, updating and improving an incomplete and partially incorrect knowledge base (KB). The main claim of our approach is that the system will start with poor knowledge, provided by the expert or the organization to which he belongs. A machine learning technique will evolve it to an incomplete KB, which may be used for further interactions with the expert, that will incrementally extend and improve it until obtaining a complete KB (i.e., with complete inferential capabilities).

Intelligent surveillance system with integration of heterogeneous information for intrusion detection

Recently, interest about security in public and private spaces has increased in favour of social welfare. Surveillance systems are increasingly needed to provide security for citizens and infrastructures. Currently there are many buildings that are equipped with cameras, sensors or microphones. However, it is difficult to find tools that integrate the information from these sources in a homogeneous system. On the other hand, the intruder detection is increasingly demanded in the corporate, commercial or private sector. For these reasons, we propose a multi-sensor intelligent system that uses information from several sources analysis (video, audio and other sensors) to identify dangerous or interest intrusions. So, we have designed a generic ontology that allows to integrate in a homogeneous way all the input heterogeneous knowledge. To perform the intrusion analysis, we propose a rule-based model, which process all the information obtained from the monitored environment. This model is easily customizable and adjustable, since the rules that define an intrusion in a semantic way can be configured depending on the scenario and circumstances. The system generates an alarm whenever an intrusion is detected. Besides, this alarm is also notified via mobile devices. So, the system reports in real time according to device capabilities, generating a context-sensitive notification.

An inductive learning algorithm in fuzzy systems

Abstract The aim of this paper is to present a method for identifying the structure of a rule in a fuzzy model. For this purpose, an ATMS shall be used. An algorithm obtaining the identification of the structure will be suggested. The minimal structure of the rule (with respect to the number of variables that must appear in the rule) will be found by this algorithm. Furthermore, the identification parameters shall be obtained simultaneously. The proposed method shall be applied for classification in an example. The Iris Plant Database shall be learnt for all three kinds of plants.