From the perspective of information theory, the design of vector quantizers (VQs) in optimizing the rate distortion function has been extensively studied. In practice, however, the existing VQ algorithms, often, suffer from a number of serious problems, e.g., long search process, codebook initialization, and getting trapped in local minima, inherent to most iterative processes. The generalized Lloyd algorithm, for designing VQs with embedded k-means clustering for codebook generation has been recently used by a number of researcher for efficient image coding by quantizing wavelet decomposed subimages. We present a new approach to vector quantization by generating such multiresolution codebooks using two different neuro-fuzzy clustering techniques that eliminate the existing problems. These clustering techniques integrate fuzzy optimization constraints from the fuzzy-C-means with self-organizing neural network architectures. In one of the new clustering techniques, a new distance measure has also been introduced. The resulting multiresolution codebooks generated from the wavelet decomposed images yield significant improvement in the coding process. The signal transformation and vector quantization stages together yield, at least, 64:1 bit rate reduction with good visual quality and acceptable peak signal to noise ratio (PSNR) and mean square error (MSE). Additional bit rate reduction can be easily obtained by employing conventional entropy encoding after the quantization stage. The performance of this new VQ coding technique has been compared to that of the well-known Linde, Buzo, and Gray (LBG) - VQ for a variety of image classes. The new VQ technique demonstrated superior ability for fast convergence with minimum distortion at similar bit rate reduction then the existing VQ technique for several classes of images/signals including standard test images and medical images in terms of mean-squared error (MSE), peak-signal-to- noise-ratio (PSNR), and visual quality.

We view edge detection as a sequence of four operations: conditioning, feature extraction, blending and scaling. Understanding the geometry of the feature extraction and blending functions is the key to customized edge detection models. We examine the role of each of these components, and show how they lead to the determination of input-output data for edge detecting learning models such as neural networks and fuzzy systems. An example of constructing edge images from a digitized mammogram is given to illustrate the utility of this approach.

The paper presents a new decision fusion methodology for identifying and tracking of multiple targets in a multisensor environment. The methodology combines concepts from the fuzzy logic and evidential reasoning domains to develop an integrated approach. The core methodology assumes that the sensors provide non-crisp or fuzzy labels, i.e., provide fuzzy class membership estimates corresponding to the different decision choices. However, the methodology can be adapted to environments wherein the sensors do not offer such information but only provide a single label deemed as the most likely. This is accomplished by having a learning phase wherein the performance of the sensors as compared to the ground truth is observed and utilized to derive fuzzy membership estimates corresponding to every individual sensor-decision scenario. The tracking mechanism is designed to also maintain fuzzy membership in different classes until the membership in any one class approaches unity. The fuzzy membership vectors, corresponding to the input sensor data as well as the tracks, include a measure of ignorance. This ignorance continuously decreases for the tracks as more and more track reports are integrated into the tracks. The paper presents details of the algorithmic process along with results as applied to some real-world data that demonstrates the effectiveness of the synergistic exploitation of the fuzzy logic and evidential reasoning concepts.

The proposed accelerated fuzzy c-means (AFCM) clustering algorithm is an improved version of the fuzzy c-mean (FCM) algorithm. Each iteration of the proposed algorithm consists of the regular operations of the FCM algorithm followed by an improvement stage. Once the cluster center locations are updated by the regular FCM algorithm operations, the improvement stage shifts each cluster center farther in its respective update direction. A number of possible strategies for the shift size control are studied and evaluated. The AFCM was applied to a number of data sets, using hundreds of different initial cluster center sets, yielding reductions of 37% to 65% in the number of iterations required for convergence by a similar FCM algorithm.

Screening mammograms for microcalcifications is important labor intensive work for an expert physician. A fatigued or inexperienced person might miss an abnormal mammogram, which is why the practice of having two readers for mammograms is not uncommon. A set of 63 features extracted from 40 mammograms, each with ground truthed microcalcifications, are used for learning and testing a set of rules to classify pixels as microcalcification or normal. A decision tree is used to learn these rules. Results from applying the rules to unseen mammograms are discussed. We also discuss a method of fuzzifying the decision tree which should lead to improved classification accuracy.

In this paper, we give a theoretical analysis for a generalized fuzzy neural network created in our previous papers. This analysis includes a mathematical proof of the training formulas used by such a network. the fuzzy neural network can accept a set of possibility functions as input as well as a vector of scalar values. This network consists of three components: a parameter-computing network, a converting layer, and a standard backpropagation-based neural network. The output vector of each layer of the parameter-computing network is a possibility vector, each element of which is a possibility function. The output vector of the converting layer is a fuzzy set, which represents the class membership values. In this paper only the first two components are considered.

Repertory grids and other matrix-like structures can be used to represent knowledge and elicit knowledge from experts. A grid or matrix is a representation of a knowledge domain where the elements in the domain appear along the horizontal axis and constructs or attributes of the elements appear along the vertical axis. Each construct is rated for its presence in a given element or how much a construct applies to an element. Analysis of these ratings can determine similarities and differences between the elements. Traditionally, constructs are bipolar entities where a rating falls on a range from one pole to the other. For example, temperature may be represented by the bipolar construct hot-cold and a range of 1 to 5 in which 1 represents hot and 5 represents cold. Ratings of 2, 3, and 4 lie in-between hot and cold. Additionally, all constructs in a grid have the same range of values and the range is arbitrarily chosen. This paper presents a method for translating grid ratings into fuzzy membership values. The fuzzy membership values become the values for describing and analyzing the associations between elements. Thus, constructs no longer need to use the same scaling range and no longer need to be bipolar. A construct of an element now becomes a true attribute of an element. An attribute can be rated in its own range and with its own unit of measurement. In the previous example, the bipolar construct hot-cold becomes simply, temperature measured in degrees. Experts or users need no longer translate to an artificial rating range.

We discuss several aspects of the multimedia fuzzy controller (MFC), which can be regarded as an extension of fuzzy controllers to include multimedia rules and memberships. The practical application context is that of law enforcement technology. We show the important role of the MFC for human input controllers in replacing the numeric input of standard controllers with media input. We have shown that the two essential problems of the FMC are the measure of distances in multifeatured spaces and the input of the media instance to the controller. The latter problem has two possible solutions: searching through the media database or constructing media instances. The first approach has been investigated in connection with the creation of a synthetic lineup for eyewitness identification of suspects. We have given a prescription for engineering a synthetic lineup for practical cases of interest. We have also shown that the essentially novel characteristic of the media databases required by the MFC is their commensurability.

The development of high resolution spectrophotometers and colorimeters, combined with its portability and large data processing abilities, has made the color evaluation process easier and faster. Although these instruments are very useful for rapid pass or fail color inspections in many industries such as, the automotive industry, textile industry, etc., the final decision depends primarily upon a subjective visual assessment. Besides spectral analysis, which is useful in colorant selection, the interrelationship between various environmental factors, metamerism, and texture and composition of the material (substrate), has made visual coordination an acceptable methodology to obtain a repeatable finish and color quality. Subjective assessment in color matching, especially in colors that closely resemble one another, leads to laborious and time consuming adjustments that have to be performed to obtain the right concentration of the colorants. Color evaluation and color mixing for a given material surface are interdependent. Although there are analytical methods that provide a means for colorant analysis, their application is cumbersome and involves complex calculations. In this paper we develop a fuzzy approach to obtain optimal color correlation between visual assessment, computed color differences, and colorant composition.

In this work the effectiveness of the fuzzy Kohonen clustering network (FKCN) has been explored in two classification experiments of remote sensed data. The FKCN has been introduced in a multi-modular neural classification system for feature extraction before labeling. The unsupervised module is connected in cascade with the next supervised module, based on the backpropagation learning rule. The performance of the FKCN has been evaluated in comparison with those of a conventional Kohonen self organizing map (SOM) neural network. Experimental results have proved that the fuzzy clustering network can be used for complex data pre-processing.

Given an arbitrary fuzzy set, there are various linguistic expressions which represent different approaches to the concept of typicality and may often be transformed to suitable numerals -- typical values. These quantities can then be replaced (not uniquely) by integral forms. A more natural approach for obtaining typical values is to apply an inverse procedure: Based on the linguistic expression and the fuzzy set, a biased measure is designed such that associated integrals over the fuzzy set with respect to this measure, yields the typical value and the balance point of the set.

Words are the fundamental carriers of information. Words that refer to numbers stand apart from all other words in one respect: Numbers are concepts that lend themselves to spatial representations with exact contours. Yet the verbal definition of numbers, through which their meaning is defined, shares in a property common to all words: their verbal definition cannot be given a spatial representation with exact contours. In that definitional respect, words are not even comparable to amoebas which, although they constantly change their shapes, have clear boundaries. Words are best to be likened to patches of fog that not only change but have no strict boundaries. While this does not land all discourse in the realm of half-truths, it sets basic limits to what can be achieved by fuzzy logic and programs of artificial intelligence.

This study investigates the applicability of a multimodular neuro-fuzzy system in the multispectral analysis of magnetic resonance (MR) images of the human brain. The system consists of two components: an unsupervised neural module for image segmentation in tissue regions and a supervised module for tissue labeling. The former is the fuzzy Kohonen clustering network (FKCN). The latter is a feed-forward network based on the back-propagation learning rule. The results obtained with the FKCN have been compared with those extracted by a self organizing map (SOM). The system has been used to analyze the multispectral MR brain images of a healthy volunteer. The data set included the proton density (PD), T2, T1 weighted spin-echo (SE) bands and a new T1- weighted three dimensional sequence, i.e. the magnetization- prepared rapid gradient echo (MP-RAGE). One of the main objectives of this study has been to evaluate the usefulness of brain imaging with the MP-RAGE sequence in view of automatic tissue classification. To this purpose, a quantitative evaluation has been provided on the base of some labeled areas selected interactively by a neuro- radiologist from the input raw images. Quantitative results seem to indicate that the MP-RAGE sequence may provide higher tissue separability than the T1-weighted SE sequence.

Networks of fuzzy basis functions (FBF) characterized by singleton fuzzifier, Gaussian membership functions, product- inference, and height method defuzzifier, show interesting characteristics, including the approximation of the Bayes discriminant function. In this paper, a classifier based on a simplified FBF (SFBF) network is presented and its performances are studied in the frame work of handwritten digits recognition. The learning rules of the SFBF network are less complex than those of a FBF network, and experimental results show a significant speed-up of learning, at the cost of a small decrease of the generalization performances. Moreover, a hybrid pattern recognition scheme (HS) is proposed, based on a hierarchy of a SFBF network plus a nearest-neighbor rule (NR), that recognizes the patterns rejected by the SFBF network. This approach permits us to recover the loss in generalization exhibited by the SFBF network alone. Specifically, the efficiency of the hierarchy can be improved, since the output of SFBF network for a rejected test pattern can be used to edit the set of rejected (training set) patterns: the NR searches only for patterns belonging to classes that get the highest rates by the SFBF network.

Image compression plays a crucial role in many important and diverse applications requiring efficient storage and transmission. This work mainly focuses on a wavelet transform (WT) based compression of fingerprint images and the subsequent classification of the reconstructed images. The algorithm developed involves multiresolution wavelet decomposition, uniform scalar quantization, entropy and run- length encoder/decoder and K-means clustering of the invariant moments as fingerprint features. The performance of the WT-based compression algorithm has been compared with JPEG current image compression standard. Simulation results show that WT outperforms JPEG in high compression ratio region and the reconstructed fingerprint image yields proper classification.

Decision making is one of the major subjects of interest in physics. This is due to the intrinsic finite accuracy of measurement that leads to the possible results to span a region for each quantity. In this way, to recognize a particle type among the others by a measure of a feature vector, a decision must be made. The decision making process becomes a crucial point whenever a low statistical significance occurs as in space cosmic ray experiments where searching in rare events requires us to reject as many background events as possible (high purity), keeping as many signal events as possible (high efficiency). In the last few years, interesting theoretical results on some feedforward connectionist systems (FFCSs) have been obtained. In particular, it has been shown that multilayer perceptrons (MLPs), radial basis function networks (RBFs), and some fuzzy logic systems (FLSs) are nonlinear universal function approximators. This property permits us to build a system showing intelligent behavior , such as function estimation, time series forecasting, and pattern classification, and able to learn their skill from a set of numerical data. From the classification point of view, it has been demonstrated that non-parametric classifiers based FFCSs holding the universal function approximation property, can approximate the Bayes optimal discriminant function and then minimize the classification error. In this paper has been studied the FBF when applied to a high energy physics problem. The FBF is a powerful neuro-fuzzy system (or adaptive fuzzy logic system) holding the universal function approximation property and the capability of learning from examples. The FBF is based on product-inference rule (P), the Gaussian membership function (G), a singleton fuzzifier (S), and a center average defuzzifier (CA). The FBF can be regarded as a feedforward connectionist system with just one hidden layer whose units correspond to the fuzzy MIMO rules. The FBF can be identified both by exploiting the linguistic knowledge available (structure identification problem) and by using the information contained in a data set (parameter estimation problem). The fuzzy system has been found to be effective for the classification tasks of about 2 by 10^-3 hadron contamination at 90% of electron acceptance. A comparison between the adaptive system results and the others previous ones obtained by using both statistical and neural network based methodologies also is presented.

A neural integrated fuzzy controller (NiF-T), which integrates the fuzzy logic representation of human knowledge with the learning capability of neural networks, is developed for nonlinear dynamic control problems. The NiF-T architecture comprises three distinct parts: (1) fuzzy logic membership functions (FMF), (2) rule neural network (RNN), and (3) output-refinement neural network (ORNN). FMF are utilized to fuzzify input parameters. RNN interpolates the fuzzy rule set; after defuzzification, the output is used to train ORNN. The weights of the ORNN can be adjusted on-line to fine-tune the controller. NiF-T can be applied for a wide range of sensor-driven robotics applications, which are characterized by high noise levels and nonlinear behavior, and where system models are unavailable or are unreliable. In this paper, real-time implementations of autonomous mobile robot navigation utilizing the NiF-T are realized. Only five rules were used to train the wall following behavior, while nine were used for the hall centering. With learning capability, the robot, SMAR-T, successfully and reliably hugs wall, and locks onto hall center. For all of the described behaviors, their RNNs are trained only for a few hundred iterations and so are their ORNNs trained only for less than one hundred iterations to learn their parent rule sets.

A general-purpose fuzzy logic inference engine for real time control applications has been designed, the core of which is based on a modified reduced symmetric fuzzy singleton set (MRSFSS) structure combining the advantages of small fuzzy memory for a maximum storing capacity of 730 rule-base. The MRSFSS structure can provide up to three input variables, a maximum of nine membership functions for each input variable, and produces two output values. The innovation of FLC chip is the definition feature of the MRSFSS structure which alleviates the drawbacks of existing fuzzy inference engine and enables the entire FLC chip to be performed on a 1.2 micrometer CMOS VLSI single chip. Although the hardware of FLC engine is simplified, the structure itself can incorporate a wide class of applications since many systematic and heuristic approaches can be cast into the MRSFSS structure with an even more simplified approach and most equal performances. Moreover, a guide tour is provided through the aspects of generating the fuzzy IF-THEN rules, based on a proposed architecture for controlling a wide class of objects whose dynamics are approximated by first- order and second-order transfer functions.

Application of fuzzy logic structures in computer-aided design (CAD) of electronic systems substantially improves quality of design solutions by providing designers with flexibility in formulating goals and selecting trade-offs. In addition, the following aspects of a design process are positively impacted by application of fuzzy logic: utilization of domain knowledge, interpretation of uncertainties in design data, and adaptation of design algorithms. We successfully applied fuzzy logic structures in conjunction with constructive and iterative algorithms for selecting of design solutions for different stages of the design process. We also introduced a fuzzy logic software development tool to be used in CAD applications.

Remote sensing and especially synthetic aperture radar (SAR) are efficient tools for environmental protection. This paper gives first a brief overview about applications and basic principles of SAR. The second part of the paper describes uncertainties and ambiguities inherent in the SAR system. Concepts using fuzzy logic that are able to handle this vagueness are proposed. In image analysis the greatest advantage appears within multisensor applications. The fuzzy system considers not only the information of the various remotely sensed data but also takes their uncertainties into account. Besides their usefulness in image analysis, fuzzy systems are suitable to create a user friendly interface and an adaptive control for future remote sensing systems. The last part of the paper presents a new approach to adaptively classify SAR images. It consist of a fuzzy comparison of distributions (FCOD) and the fuzzy learning vector quantizer (FLVQ). This system performs a first step towards an improved SAR system.

This paper discusses the application of fuzzy logic to quality and reliability issues in microelectronics. After a general introduction, the potential role of fuzzy logic is reviewed at various stages of the production process: testing, process control, and design for reliability and quality.

Technology mapping for FPGAs with complex logic blocks is performed by a fuzzy logic system. A solution is constructed by a successive augmentation algorithm that employs fuzzy logic on all decision steps to balance multiple factors influencing choices. Rules are dynamically adapted when results of partial and completed mapping are compared with the stated goals for area and timing.

Consider the problem of building the map of an unknown environment by using range readings obtained through ultrasonic sensors, and assume that a bitmap representation is adopted for compactness. In an ideal map, each cell of the bitmap is either empty or occupied by an obstacle. Because of the uncertainty introduced by sonar sensing, it is necessary to process appropriately the measures in order to classify each cell with a reasonable degree of accuracy. We compare three different algorithms for ultrasonic map building that are based respectively on probability theory, fuzzy logic and fuzzy measures. Simulation results in a one- dimensional case and experimental results for an office-like environment are presented to perform a comparison among the presented approaches.

Fuzzy controllers make transformations from qualitative rules into numerical (corresponding) mappings; while fuzzy information compression mainly make transformation from numerical data into qualitative rules. The core of ideas of fuzzy computing is the quantitative-qualitative transformation based on fuzzy logic.

Research of a fuzzy logic (FL) controller to perform commercial truck anti-skid braking (ABS) has been completed. Via quarter-model simulation, the FL ABS braking performance demonstrates a 30% improvement over the currently fielded finite state (FS) ABS controller. Significance of this improvement is determined by comparing braking distances to a theoretical lower bound. The next step in the ABS product improvement cycle is the functional replacement of the FS with the FL control algorithm. The functional replacement is constrained by the current form, fit and function of the existing fielded package. Thus, a 'sizing' of the FL controller must balance this 30% improvement in braking distance against the performance constraints imposed by the current memory size, memory speed, processor architecture, and processor speed of the fielded system. This FL case study provides an opportunity to identify 'sizing' issues as they relate to fuzzy logic, and in particular, as they relate to limited memory.

According to the following definition, taken from the literature, a fuzzy clustering mechanism allows the same input pattern to belong to multiple categories to different degrees. Many clustering neural network (NN) models claim to feature fuzzy properties, but several of them (like the Fuzzy ART model) do not satisfy this definition. Vice versa, we believe that Kohonen's Self-Organizing Map, SOM, satisfies the definition provided above, even though this NN model is well-known to (robustly) perform topologically ordered mapping rather than fuzzy clustering. This may sound as a paradox if we consider that several fuzzy NN models (such as the Fuzzy Learning Vector Quantization, FLVQ, which was first called Fuzzy Kohonen Clustering Network, FKCN) were originally developed to enhance Kohonen's models (such as SOM and the vector quantization model, VQ). The fuzziness of SOM indicates that a network of processing elements (PEs) can verify the fuzzy clustering definition when it exploits local rules which are biologically plausible (such as the Kohonen bubble strategy). This is equivalent to state that the exploitation of the fuzzy set theory in the development of complex systems (e.g., clustering NNs) may provide new mathematical tools (e.g., the definition of membership function) to simulate the behavior of those cooperative/competitive mechanisms already identified by neurophysiological studies. When a biologically plausible cooperative/competitive strategy is pursued effectively, neighboring PEs become mutually coupled to gain sensitivity to contextual effects. PEs which are mutually coupled are affected by vertical (inter-layer) as well as horizontal (intra-layer) connections. To summarize, we suggest to relate the study of fuzzy clustering mechanisms to the multi-disciplinary science of complex systems, with special regard to the investigation of the cooperative/competitive local rules employed by complex systems to gain sensitivity to contextual effects in cognitive tasks. In this paper, the FLVQ model is critically analyzed in order to stress the meaning of a fuzzy learning mechanism. This study leads to the development of a new NN model, termed the fuzzy competitive/cooperative Kohonen (FCCK) model, which replaces FLVQ. Then, the architectural differences amongst three NN algorithms and the relationships between their fuzzy clustering properties are discussed. These models, which all perform on-line learning, are: (1) SOM; (2) FCCK; and (3) improved neural-gas (INC).