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Fuzzy sets of rules for system identification
R. Rovatti, R. Guerrieri
vol. 4, no. 2, pp. 89-102, May 1996

The synthesis of fuzzy systems involves the identification of a structure and its specialization by means of parameter optimization. In doing this, symbolic approaches which encode the structure information in the form of high-level rules allow further manipulation of the system to minimize its complexity, and possibly its implementation cost, while all-parametric methodologies often achieve better approximation performance. In this paper, we rely on the concept of a fuzzy set of rules to tackle the rule induction problem at an intermediate level. An online adaptive algorithm is developed which almost surely learns the extent to which inclusion of a rule in the rule set significantly contributes to the reproduction of the target behavior. Then, the resulting fuzzy set of rules can be defuzzified to give a conventional rule set with similar behavior. Comparisons with high-level and low-level methodologies show that this approach retains the most positive features of both.

Fuzzy logic = computing with words
L. A. Zadeh
vol. 4, no. 2, pp. 103-11, May 1996

As its name suggests, computing with words (CW) is a methodology in which words are used in place of numbers for computing and reasoning. The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa. Thus, as an approximation, fuzzy logic may be equated to CW. There are two major imperatives for computing with words. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers, and second, when there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality. Exploitation of the tolerance for imprecision is an issue of central importance in CW. In CW, a word is viewed as a label of a granule; that is, a fuzzy set of points drawn together by similarity, with the fuzzy set playing the role of a fuzzy constraint on a variable. The premises are assumed to be expressed as propositions in a natural language. In coming years, computing with words is likely to evolve into a basic methodology in its own right with wide-ranging ramifications on both basic and applied levels.

Validity-guided (re)clustering with applications to image segmentation
A. M. Bensaid, L. O. Hall, J. C. Bezdek, L. P. Clarke, M. L. Silbiger, J. A. Arrington, R. F. Murtagh
vol. 4, no. 2, pp. 112-23, May 1996

When clustering algorithms are applied to image segmentation, the goal is to solve a classification problem. However, these algorithms do not directly optimize classification duality. As a result, they are susceptible to two problems: 1) the criterion they optimize may not be a good estimator of "true" classification quality, and 2) they often admit many (suboptimal) solutions. This paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2. The validity-guided (re)clustering (VGC) algorithm uses cluster-validity information to guide a fuzzy (re)clustering process toward better solutions. It starts with a partition generated by a soft or fuzzy clustering algorithm. Then it iteratively alters the partition by applying (novel) split-and-merge operations to the clusters. Partition modifications that result in improved partition validity are retained. VGC is tested on both synthetic and real-world data. For magnetic resonance image (MRI) segmentation, evaluations by radiologists show that VGC outperforms the (unsupervised) fuzzy c-means algorithm, and VGC`s performance approaches that of the (supervised) k-nearest-neighbors algorithm.

Fuzzy modeling and analytic hierarchy processing to quantify risk levels associated with occupational injuries. I. The development of fuzzy-linguistic risk levels
P. McCauley-Bell, A. B. Badiru
USA
vol. 4, no. 2, pp. 124-31, May 1996

This paper presents the Part I in a two-phase research project to develop a fuzzy-linguistic expert system for quantifying and predicting the risk of occupational injury, specifically, cumulative trauma disorders of the forearm and hand. This aspect of the research focuses on the development and representation of linguistic variables to qualify risk levels. These variables are then quantified using fuzzy-set theory, thus allowing the model to evaluate qualitative and quantitative data. These linguistic risk variables may be applied to other potentially hazardous environments. The three phases of the knowledge acquisition and variable development are covered, as well as the feasibility of the linguistic variables.

Fuzzy modeling and analytic hierarchy processing-means to quantify risk levels associated with occupational injuries. II. The development of a fuzzy rule-based model for the prediction of injury
P. McCauley-Bell, A. B. Badiru
USA
vol. 4, no. 2, pp. 132-8, May 1996

This paper presents the second phase in a two-part research project to develop a fuzzy rule-based expert system for predicting occupational injuries of the forearm and hand. Analytic hierarchy processing (AHP) is used to assign relative weights to the identified risk factors. A fuzzy rule base is constructed with all of the potential combinations for the given factors. The input parameters are linguistic variables obtained in the first part of the research. These inputs are fuzzified and defuzzified to provide two system outputs: a linguistic value and a numeric value as a prediction of injury. The system provides linguistic risk levels as well as quantified risks in assessing the overall risk of injury. The system evaluation was conducted resulting in calculations for Type I and Type II errors. The contributions and limitations of the system are discussed.

Fuzzy multimodels
W. Pedrycz
vol. 4, no. 2, pp. 139-48, May 1996

Fuzzy multimodeling is concerned with the design and utilization of families rather than a single model. The intent is to approximate data that are originated by phenomena whose nature is more relation based than function oriented. In general, fuzzy multimodels comprise a collection of local models M/sub 1/, M/sub 2/,...,M/sub C/ along with the relevant mechanisms of their triggering and aggregating, aimed at assuring a suitable interaction between these models. The idea of multimodeling is contrasted with some other approaches to fuzzy modeling available in the current literature. The algorithmic details are laid down and illustrated through several detailed simulation studies.

Decomposition property of fuzzy systems and its applications
Jun Zeng Xiao, M. G. Singh
vol. 4, no. 2, pp. 149-65, May 1996

This paper presents the decomposition property of fuzzy systems using a simple, constructive, decomposition procedure. That is, by properly dividing the input space into sub-input spaces, a general fuzzy system is decomposed into several sub-fuzzy systems which are the simplest fuzzy systems in the sub-input spaces. Based on the decomposition property of fuzzy systems, the analysis of fuzzy systems can be divided into two steps: first, analyze the properties of the simplest fuzzy systems, and then, use the decomposition property to extend the results to general fuzzy systems. Using this idea, two applications of the decomposition property are given. The first is the application to the representation capability analysis of fuzzy systems. The second is the application to the analysis of a class of nonlinear control systems. Then, based on the piecewise affine fuzzy-system model, the existence condition and the design of a stable control for a class of single-input single-output (SISO) nonlinear systems are presented.

A new methodology of fuzzy constraint-based controller design via constraint-network processing
Yu Tyan Ching, P. P. Wang, D. R. Bahler, S. P. Rangaswamy
vol. 4, no. 2, pp. 166-78, May 1996

A complete design framework for a fuzzy constraint-based controller based on fuzzy-constraint processing and its semantics and relationship to fuzzy logic is presented. In this paper, the concept of "fuzzy constraints" in problem solving is introduced, and some basic definitions of fuzzy-constraint processing in a constraint network and its semantic modeling are addressed. Then a fuzzy local propagation inference mechanism for reasoning about imprecise information applying the filter operation in a network of constraints is proposed. Moreover, we advance the concurrent fuzzy-logic controller (FLC) to a new type of controller, the fuzzy constraint-based controller (FCC), using a more general predicate calculus and full first-order logic knowledge representation and making use of the idea of fuzzy-constraint processing to model practical dynamic control systems. Finally, simulation results show that a FCC achieves equivalent performance as PD type and PI type FLCs and it also demonstrates superior outcomes to a conventional PID controller in terms of rise time and peak-percent overshoot.