Adolf Grauel

Construction of differentiable membership functions

In many applications of fuzzy logic it is of special interest to have a transfer function with good properties regarding differentiability. To that end it is desirable to have continuously differentiable membership functions with only few parameters. In this paper we propose a class of symmetrical and asymmetrical membership functions of exponential order. Moreover, we present a class of more flexible membership functions by construction.

Mathematical analysis of the Sugeno controller leading to general design rules

Abstract The Sugeno controller is one of the widest spread Fuzzy controllers. In this paper we investigate the analytical behaviour of the transfer function, especially the connection between the shape of the transfer function and the shape of the membership functions. Based on the results, common membership functions are examined for multi-input controllers and design rules are derived.

Comparison of different intelligent methods for process and quality monitoring

Abstract We compare three computer-aided systems used for on-line process and quality monitoring in metal processing industries. In a running manufacturing process measurement data are taken, from which significant quality statements are extracted. For this we apply on one hand an artificial neural network, which learns to classify the data adequately by using given exemplary process states; on the other hand we designed a fuzzy logic system that carries out the same task knowledge-based. Furthermore we present investigations of fuzzy clustering techniques to obtain information about the process. Moreover, topology optimization by evolutionary algorithms is considered to obtain optimal structures of the multilayer perceptron used. The quality features extracted are then passed on to the next hierarchical level, where they are processed within the framework of an integrated manufacturing and quality control system.

Optimizing fuzzy classifiers by evolutionary algorithms

In this paper a methodology for optimizing fuzzy classifiers based on B-splines by evolutionary algorithms is presented. The algorithm proposed maximizes the performance and minimizes the size of the classifier. On a well-known classification problem the algorithm using only part of the features has a recognition rate comparable to an LDA on the total feature space.

The Painleve test, Backlund transformation and solutions of the reduced Maxwell-Bloch equations

The Painleve property for partial differential equations (PDES) proposed by Weiss et al. (1983) is studied for a system of PDES, namely the reduced Maxwell-Bloch (RMB) equations. The RMB equations describe the propagation of short optical pulses through dielectric materials with a resonant non-degenerate transition. The author demonstrates that the RMB system passes the Painleve test, and constructs a Backlund transformation and solutions of the RMB equations.

A New Paradigm of Optimisation by Using Artificial Immune Reactions

This paper presents an implementation of an artificial immune system in order to realise multi-modal function optimisation. The main paradigms of an artificial immune system are clonal selection and affinity maturation. Therefore these paradigms are reviewed briefly. The optimisation is based on the opt-aiNet algorithm. This algorithm is described theoretically. Furthermore, the Griewank function has been used to test the algorithm with different parameters. The simulation results are discussed.

ECG diagnostics by fuzzy decision making

The analysis of electrocardiograms (ECGs) helps physicians make their cardiac diagnosis. Therefore a large store of medical knowledge and practical experience is required. In this paper we report on our investigations of a rule-based fuzzy logic system that processes ECG data using the knowledge of a medical expert. The aim is to give support to the physician for his diagnosis. In this first consideration we discuss single modules of the rule-based system proposed and moreover we present the used input and output variables of the rulebases. The performance of the implemented rule-based fuzzy logic system is tested using ECGs with abnormalities in the P and T wave as well as in the QRS complex. The systems output corresponds to the analysis of these ECGs by a medical expert.

Gaussians-Based Hybrid System for Prediction and Classification

We propose a hybrid model based on Genetic Algorithms (GA), Lattice Based Associative Memory Networks (LB-AMN) and Radial Basis Function Networks (RBFN) for the solution of prediction and classification problems. LB-AMN and RBFN have as basis in their structure a type of asymmetric radial basis function (RBF) which results from the combination of two Gaussian functions. In the first sections we describe the mathematical models used to build the hybrid system. Afterwards, we apply the model to the problem of breast cancer and toxicity prediction. In both cases, the obtained results were better than the ones obtained using other approaches. Finally, some conclusions are given.

Data Mining and Automation of Experts Decision Process Applied to Machine Design for Furniture Production

A software concept based on data mining and knowledge discovery for a multi-spindle drilling gear configuration and optimisation applied to a machine used in furniture production process is proposed. The objective is to find the minimum number of supports and the optimised configuration of the multi-spindle drilling gears. Intelligent analysis of input data and an automated system covering the human design procedure are applied to configure multi-drilling gears. The input data presented as digitalised customer engineering drawings and furthermore technology data describing the basic constraints of the machine construction are presented. Moreover the transfer of acquired manual design experience from a human expert to a software strategy to solve the multi-criteria optimisation problem is shown.

Optimizing lattice-based associative memory networks by evolutionary algorithms

Abstract Problem specific network structure optimization subsumes the problem of input selection and network topology identification. Requirements to the network should be accuracy and good generalization abilities. In this contribution we describe in detail an evolutionary algorithm which performs both tasks well. Furthermore, approximation results on mathematical and real world data are presented. In this case we used lattice-based associative memory networks (LB-AMNs) using B-splines as basis functions. The method here is not restricted to B-splines as basis functions. The proposed method and algorithm can be seen as optimized classification system.