Fusion of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) have attracted the growing interest of researchers in various scientific and engineering areas due to the growing need of adaptive intelligent systems to solve the real world problems. ANN learns from scratch by adjusting the interconnections between layers. FIS is a popular computing framework based on the concept of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. The advantages of a combination of ANN and FIS are obvious. There are

A methodology for the development of linguistically interpretable fuzzy models from data is presented. The implementation ofthe model is conducted through the training ofa neuro-fuzzy network, i.e., a neural net architecture capable ofrepresenting a fuzzy system. In the rst phase, the structure ofthe model is obtained by means ofsubtractive clustering, which allows the extraction ofa set ofrelevant rules based on a set ofrepresentative input–output data samples. In the second phase, the parameters ofthe model are tuned via the training ofa neural network through backpropagation. In order to attain interpretability goals, the method proposed imposes some constraints on the tuning ofthe parameters and performs membership function merging. In this way, it will be easy to assign linguistic labels to each of the membership functions obtained, after training. Therefore, the model obtained for the system under analysis will be described by a set oflinguistic rules, easily interpretable.

Within the Linguistic Modeling eld |one of the most important applications of Fuzzy Rule-Based Systems|, a family of ecient and simple methods guided by covering criteria of the data in the example set, called \ad hoc data-driven methods", has been proposed in the literature in the last few years. Their high performance, in addition to their quickness and easy understanding, have make them very suitable for learning tasks. In this paper we are going to perform a double task analyzing these kinds of learning methods and introducing a new methodology to signicantly improve their accuracy keeping their descriptive power unalterable. On the one hand, a taxonomy of ad hoc data-driven learning methods based on the way in which the available data is used to guide the learning will be made. In this sense, we will distinguish between two approaches: the example-based and the fuzzy-grid-based one. Whilst in the former each rule is obtained from a specic example, in the latter the e...

During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides human-friendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. It is observed, however, that transparency, which is vital for undistorted information transfer, is not a default property of fuzzy systems, moreover, application of algorithms that identify fuzzy systems from data will most likely destroy any semantics a fuzzy system ever had after initialization. This thesis thoroughly investigates the issues related to transparency. Fuzzy systems are generally divided into two classes. It is shown here that for these classes different definitions of transparency apply. For standard fuzzy systems that use fuzzy propositions in IF-THEN rules, explicit transparency constraints have been derived. Based on these constraints, exploitation/modification schemes of existing identification algorithms are suggested, moreover, a new algorithm for training standard fuzzy systems has been proposed, with a considerable potential to reduce the gap between accuracy and transparency in fuzzy modeling. For 1st order Takagi-Sugeno systems that are interpreted in terms of local linear models, such conditions cannot be derived due to system architecture and its undesirable interpolation properties of 1st order TS systems. It is, however, possible to solve the transparency preservation problem in the context of modeling with another proposed method that benefits from rule activation degree exponents. 1st order TS systems that admit valid interpretation of local models as linearizations of the modeled system are useful, for example, in gain-scheduled control. Transparent standard fuzzy systems, on the other hand, are vital to this branch of intelligent control that seeks solutions by emulating the mechanisms of reasoning and decision processes of human beings not limited to knowledge-based fuzzy control. Performing the local inversion of the modeled system it is possible to extract relevant control information, which is demonstrated with the application of fed-batch fermentation. The more a fuzzy controller resembles the expert’s role in a control task, the higher will be the implementation benefit of the fuzzy engine. For example, a hierarchy of fuzzy (and non-fuzzy) controllers simulates an existing hierarchy in the human decision process and leads to improved control performance. Another benefit from hierarchy is that it assumes problem decomposition. This is especially important with fuzzy logic where large number of system variables leads to exponential explosion of rules (curse of dimensionality) that makes controller design extremely difficult or even impossible. The advantages of hierarchical control are illustrated with truck backer-upper applications.

The integration of neural networks and fuzzy inference systems could be formulated into three main categories: cooperative, concurrent and integrated neuro-fuzzy models. We present three different types of cooperative neurofuzzy models namely fuzzy associative memories, fuzzy rule extraction using self-organizing maps and systems capable of learning fuzzy set parameters. Different Mamdani and Takagi-Sugeno type integrated neuro-fuzzy systems are further introduced with a focus on some of the salient features and advantages of the different types of integrated neuro-fuzzy models that have been evolved during the last decade. Some discussions and conclusions are also provided towards the end of the chapter.

Abstract. System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years. The chapter analyzes mechanisms to find this balance by improving the accuracy in linguistic FM: deriving the membership functions, improving the fuzzy rule set derivation, or extending the model structure. 1

This paper reviews neuro-fuzzy systems, which combine methods from neural network theory with fuzzy systems. Such combinations have been considered for several years already. However, the term neuro-fuzzy still lacks proper definition, and still has the flavour of a buzzword to it. Surprisingly few neuro-fuzzy approaches do actually employ neural networks, even though they are very often depicted in form of some kind of neural network structure. However, all approaches display some kind of learning capability, as it is known from neural networks. This means, they use algorithms which enable them to determine their parameters from training data in an iterative process. In this paper we review some of our neuro-fuzzy approaches to illustrate our view of neuro-fuzzy techniques and our understanding on how these approaches should be used. From our point of view neuro-fuzzy means using heuristic learning strategies derived from the domain of neural network theory to support the developmen...

This article provides over one hundred references to works in the medical domain using evolutionary computation

Fuzzy Rule-Based Systems with a better trade-off between interpretability and accuracy in linguistic fuzzy modelling problems. To do that, we present a new post-processing method that by considering selection of rules together with tuning of membership functions gets solutions only in the Pareto zone with the highest accuracy, i.e., containing solutions with the least number of possible rules but still presenting high accuracy. This method is based on the well-known SPEA2 algorithm, applying appropriate genetic operators and including some modifications to concentrate the search in the desired Pareto zone.

Both general fuzzy systems and most neural networks are universal approximators in the sense that they are capable of approximating any continuous function with arbitrary accuracy with respect to, e.g., the supremum norm. It means that these techniques share approximation capabilities. However, the way they captures the underlying transfer function is different. Fuzzy systems operating with if-then rules have the advantage of easy linguistic interpretability, while neural networks can adapt learning methods to improve their performance according to a training data set. We point out in this paper that several fuzzy controllers implement one of the typical neural networks (having radial basis type activation functions), and hence, their combination may alloy the the advantageous properties of the two techniques.