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SQLf: a relational database language for fuzzy querying
P. Bosc, O. Pivert
vol. 3, no. 1, pp. 1-17, Feb. 1995

An important issue in extending database management systems functionalities is to allow the expression of imprecise queries to enable these systems to satisfy the user needs more closely. This paper deals with imprecise querying of regular relational databases. The basic idea is to extend an existing query language, namely SQL. In this context, two important points must be considered: one concerns the integration in the extended language of many propositions that have been made elsewhere, in particular those concerning fuzzy aggregation operators; and the second point is to know whether the equivalences which are valid in SQL still hold in the extended language. Both these topics are investigated in this paper.

A method for fuzzy rules extraction directly from numerical data and its application to pattern classification
S. Abe, Shong Lan Ming
vol. 3, no. 1, pp. 18-28, Feb. 1995

In this paper, we discuss a new method for extracting fuzzy rules directly from numerical input-output data for pattern classification. Fuzzy rules with variable fuzzy regions are defined by activation hyperboxes which show the existence region of data for a class and inhibition hyperboxes which inhibit the existence of data for that class. These rules are extracted from numerical data by recursively resolving overlaps between two classes. Then, optimal input variables for the rules are determined using the number of extracted rules as a criterion. The method is compared with neural networks using the Fisher iris data and a license plate recognition system for various examples.

Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. I
R. Krishnapuram, H. Frigui, O. Nasraoui
vol. 3, no. 1, pp. 29-43, Feb. 1995

Traditionally, prototype-based fuzzy clustering algorithms such as the Fuzzy C Means (FCM) algorithm have been used to find "compact" or "filled" clusters. Recently, there have been attempts to generalize such algorithms to the case of hollow or "shell-like" clusters, i.e., clusters that lie in subspaces of feature space. The shell clustering approach provides a powerful means to solve the hitherto unsolved problem of simultaneously fitting multiple curves/surfaces to unsegmented, scattered and sparse data. In this paper, we present several fuzzy and possibilistic algorithms to detect linear and quadric shell clusters. We also introduce generalizations of these algorithms in which the prototypes represent sets of higher-order polynomial functions. The suggested algorithms provide a good trade-off between computational complexity and performance, since the objective function used in these algorithms is the sum of squared distances, and the clustering is sensitive to noise and outliers. We show that by using a possibilistic approach to clustering, one can make the proposed algorithms robust.

A self-organizing fuzzy logic controller for dynamic systems using a fuzzy auto-regressive moving average (FARMA) model
Moon Park Young, Chul Moon Un, K. Y. Lee
vol. 3, no. 1, pp. 75-82, Feb. 1995

The paper proposes a complete design method for an online self-organizing fuzzy logic controller without using any plant model. By mimicking the human learning process, the control algorithm finds control rules of a system for which little knowledge has been known. In a conventional fuzzy logic control, knowledge on the system supplied by an expert is required in developing control rules, however, the proposed new fuzzy logic controller needs no expert in making control rules, Instead, rules are generated using the history of input-output pairs, and new inference and defuzzification methods are developed. The generated rules are stored in the fuzzy rule space and updated online by a self-organizing procedure. The validity of the proposed fuzzy logic control method has been demonstrated numerically in controlling an inverted pendulum.

A fuzzy logic system for the detection and recognition of handwritten street numbers
P. Gader, J. M. Keller, J. Cai
vol. 3, no. 1, pp. 83-95, Feb. 1995

Fuzzy logic is applied to the problem of locating and reading street numbers in digital images of handwritten mail. A fuzzy rule-based system is defined that uses uncertain information provided by image processing and neural network-based character recognition modules to generate multiple hypotheses with associated confidence values for the location of the street number in an image of a handwritten address. The results of a blind test of the resultant system are presented to demonstrate the value of this new approach. The results are compared to those obtained using a neural network trained with backpropagation. The fuzzy logic system achieved higher performance rates.

On equivalence classes of fuzzy connectives-the case of fuzzy integrals
M. Grabisch
vol. 3, no. 1, pp. 96-109, Feb. 1995

An equivalence relation between connectives (or operators) in the framework of multiple criteria decision-making is introduced. Two operators are said to be equivalent if they lead to the same ranking of alternatives. Some general results to find equivalence classes of operators are given through the concept of level surfaces. In a second part, these results are applied to the case of discrete fuzzy integrals, which are considered here as n-place operators. First, some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals.

A note on fuzzy set theory in scanning
H. Bandemer, A. Kraut
vol. 3, no. 1, pp. 110-15, Feb. 1995

Scanning of a natural picture handled by an image processing system always causes a loss of information, i.e., the micro picture elements become uncertain and vague. This is essential when the picture is to be used for measuring or evaluation of structural parameters. To make the induced uncertainty and vagueness transparent up to the computed results, specifications and procedures from fuzzy set theory are presented and suggested. In particular, distances of pixels are considered. For a demonstration of how this uncertainty can influence conclusions from the given picture, the computation of the approximate gradient of a curve is considered.

Scaling of fuzzy controllers using the cross-correlation
R. Palm
vol. 3, no. 1, pp. 116-23, Feb. 1995

The paper deals with the optimal adjustment of input scaling factors for fuzzy controllers (FCs). The method is based on the assumption that in the stationary case an optimally adjusted input scaling factor meets a specific statistical input output dependence. A measure for the strength of statistical dependence is the correlation function and the correlation coefficient, respectively. Without loss of generality, the adjustment of input scaling factors using correlation functions is pointed out by means of a single input-single output (SISO)-system. First, the paper deals with the so-called equivalent gain which is closely connected to the cross-correlation of the controller input and the defuzzified controller output. Next, it considers the computation of correlation functions and their representation inside the FC. The paper concludes with an example of a system of fuzzy rules controlling a redundant robot manipulator.

Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. II
R. Krishnapuram, H. Frigui, O. Nasraoui
vol. 3, no. 1, pp. 44-60, Feb. 1995

Shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation, particularly when the boundaries have jagged or scattered edges and when the range data is sparse. This is because shell clustering is insensitive to local aberrations, it can be performed directly in image space, and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals. The shell clustering algorithms introduced in Part I of this paper assume that the number of clusters is known, however, which is not the case in many boundary detection and surface approximation applications. This problem can be overcome by considering cluster validity. We introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper, we show through theoretical derivations that surface density is relatively invariant to size and partiality (incompleteness) of the clusters. We describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically, and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images.

Synthesis of operational transconductance amplifier-based analog fuzzy functional blocks and its application
K. Tsukano, T. Inoue
vol. 3, no. 1, pp. 61-8, Feb. 1995

A synthesis of analog fuzzy functional blocks (a complementary membership function circuit, a maximum circuit, a complementary maximum circuit, and a defuzzifier circuit) based on operational transconductance amplifiers (OTA's) is presented. The complementary membership function circuit and the maximum circuit are synthesized from the formulations using bounded-difference operations. The defuzzifier circuit is synthesized as the follower-aggregation circuit composed of multiplier-type OTA's, SPICE simulations showed that the proposed fuzzy functional blocks feature high-speed operations and low power consumption. The complementary membership function circuit, the maximum circuit, and the complementary maximum circuit were built with discrete components and commercially available OTA's, and the performances of these circuits were confirmed by experiments. As an application, a singleton fuzzy controller with 3*3 rules is synthesized using the proposed circuits. The simulation of this controller showed that the inference speed of the order of 15 MRPS (rules per second) is easily realizable.

Fuzzy automata with fuzzy relief
J. Virant, N. Zimic
vol. 3, no. 1, pp. 69-74, Feb. 1995

This paper shows a definition of a fuzzy automaton, which has the state, input, and output sets as fuzzy sets. The state transition function is defined as moving on a fuzzy relief with fuzzy peak-states and boundaries between different membership functions. After the definition of fuzzy automaton with fuzzy relief, the paper deals with a generalization, simulation and realization of such a fuzzy automaton. The paper links the defined fuzzy automaton to an existing fuzzy JK memory cell and to well-known fuzzy automata defined on the basis of crisp sets.