Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (Adaptive-Network-based Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory, bayesian-based reasoning, belief networks, fuzzy logics etc. We propose rough mereology as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes approximate proofs understood as schemes constructed to support our assertions about the world on the basis of our incomplete or uncertain knowledge. 1 Introduction We present a formal model of approximate reasoning about processes of synthesis of complex systems. First ideas of this approach have been presented in [15], [24], [25], [27], [28], [29], [30], [31]. Our research has been stimulated by the demand for solutions of the following groups of problems, estimated in [1] to be crucial for the progress in the area of automated design and manufacturing. These groups of problems are concerned with the treatment of: Group 1. Poorly defined...

Nowadays Fuzzy Logic Controllers have been succesfully applied to a wide range of engineering control processes. Several tasks have to be performed in order to design an intelligent control system of this kind for a concrete application. One of the most important and difficult ones is the extraction of the expert known knowledge of the controlled system. The aim of this paper is to present an evolutionary process based on genetic algorithms and evolution strategies for learning the Fuzzy Logic Controller Knowledge Base from examples in three different stages. The process allows us to generate two different kinds of Knowledge Bases, descriptive and approximative ones, depending on the scope of the fuzzy sets giving meaning to the fuzzy control rule linguistic terms, taking preliminary linguistic variable

The term Soft Computing (SC) represents the combination of emerging problem-solving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, real-world problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagation-type algorithms.

In this paper, we present MLEANN (Meta-Learning Evolutionary Artificial Neural Network), an automatic computational framework for the adaptive optimization of artificial neural networks wherein the neural network architecture, activation function, connection weights; learning algorithm and its parameters are adapted according to the problem. We explored the performance of MLEANN and conventionally designed artificial neural networks for function approximation problems. To evaluate the comparative performance, we used three different well-known chaotic time series. We also present the state of the art popular neural network learning algorithms and some experimentation results related to convergence speed and generalization performance. We explored the performance of backpropagation algorithm; conjugate gradient algorithm, quasi-Newton algorithm and Levenberg-Marquardt algorithm for the three chaotic time series. Performances of the different learning algorithms were evaluated when the activation functions and architecture were changed. We further present the theoretical background, algorithm, design strategy and further demonstrate how effective and inevitable is the proposed MLEANN framework to design a neural network, which is smaller, faster and with a better generalization performance.

It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective. Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU. In GTU, a probabilistic constraint is viewed as a special––albeit important––instance of a generalized constraint. A generalized constraint is a constraint of the form X isr R, where X is the constrained variable, R is a constraining relation, generally non-bivalent, and r is an indexing variable which identifies the modality of the constraint, that is, its semantics. The

An importance of the idea of granularity of knowledge for approximate reasoning has been recently stressed in [6,9-10]. We address here the problem of synthesis of adaptive decision algorithms and we propose an approach to this problem based on the notion of a granule which we develop in the framework of rough mereology. This framework does encompass both rough and fuzzy set theories. Our approach may be applied in the problems of approximate synthesis of complex objects (solutions) in distributed systems of intelligent agents. Keywords--- rough sets, apporoximate reasoning, rough mereology, granules of knowledge I. Introduction: a notion of a granule In this introduction, we first present the rough set approach, then we outline the fuzzy set approach and finally we introduce elements of rough mereological theory [2], [7,8] by means of which we will define in the sequel the notion of a granule of knowledge in a unified way. We begin with rough set approach [5]. In this approach, kn...

In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such rules by means of appropriate quality measures is less obvious. Particularly, it assumes an understanding of the semantic meaning of a fuzzy rule. This aspect has been ignored by most existing proposals, which must therefore be considered as ad-hoc to some extent. In this paper, we develop a systematic approach to the assessment of fuzzy association rules. To this end, we proceed from the idea of partitioning the data stored in a database into examples of a given rule, counterexamples, and irrelevant data. Evaluation measures are then derived from the cardinalities of the corresponding subsets. The problem of finding a proper partition has a rather obvious solution for standard association rules but becomes less trivial in the fuzzy case. Our results not only provide a sound justification for commonly used measures but also suggest a means for constructing meaningful alternatives.

The aim of this paper is to present an evolutionary process based on genetic algorithms and evolution strategies for learning the Fuzzy Logic Controller Knowledge Base from examples. The performance of the method proposed is shown by measuring the accuracy of the Fuzzy Logic Controllers designed in the modeling of two three-dimensional control surfaces derived from two mathematical functions presenting different characteristics. The results obtained by a method based on the Wang and Mendel's Knowledge Base generation process are also shown, allowing to compare both processes.

Abstract: The integration of different learning and adaptation techniques to overcome individual limitations and to achieve synergetic effects through the hybridization or fusion of these techniques has, in recent years, contributed to a large number of new intelligent system designs. Computational intelligence is an innovative framework for constructing intelligent hybrid architectures involving Neural Networks (NN), Fuzzy Inference Systems (FIS), Probabilistic Reasoning (PR) and derivative free optimization techniques such as Evolutionary Computation (EC). Most of these hybridization approaches, however, follow an ad hoc design methodology, justified by success in certain application domains. Due to the lack of a common framework it often remains difficult to compare the various hybrid systems conceptually and to evaluate their performance comparatively. This chapter introduces the different generic architectures for integrating intelligent systems. The designing aspects and perspectives of different hybrid archirectures like NN-FIS, EC-FIS, EC-NN, FIS-PR and NN-FIS-EC systems are presented. Some conclusions are also provided towards the end.