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Designing fuzzy logic controllers using a multiresolutional search paradigm
Kim Jinwoo, B. P. Zeigler
Dept. of Electr. & Comput. Eng., Arizona Univ., Tucson, AZ, USA
vol. 4, no. 3, pp. 213-26, Aug. 1996

A multiresolutional search paradigm is employed to design optimal fuzzy logic controllers in a variable structure simulation environment. The initial search space is evaluated with a coarse resolution and some of the subspaces are selected as candidate regions for global optimum. New optimization processes are then created to investigate the candidate search spaces in detail, a process which continues until a solution is found. This search paradigm was implemented using hierarchical distributed genetic algorithms (HDGAs)-search agents solving different degrees of abstracted problems. Creation/destruction of agents is executed dynamically during the operation based on their performance. In the application to fuzzy systems, the HDGA investigates design alternatives such as different types of membership functions and the number of the fuzzy labels, as well as their optimal parameter settings, all at the same time. This paradigm is demonstrated with an application to the design of a fuzzy controller for an inverted pendulum.

A unifying approach to defuzzification and comparison of the outputs of fuzzy controllers
J. J. Saade
Dept. of Electr. & Comput. Eng., American Univ. of Beirut, Lebanon
vol. 4, no. 3, pp. 213-26, Aug. 1996

This paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective. This is done by emphasizing the fuzzy controller as a decision-making system. Based on the extensive study and justification of the fuzzy-set comparison criteria that were developed and published elsewhere by the author, a ranking and, thus, a defuzzification index is introduced. This index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful. In addition, the proposed index is based on the generalization of the Hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases.

Handling uncertainty with possibility theory and fuzzy sets in a satellite fault diagnosis application
D. Cayrac, D. Dubois, H. Prade
Oper. Support & Mission Optimization Dept., Matra Marconi Space, Toulouse, France
vol. 4, no. 3, pp. 251-69, Aug. 1996

The fault mode effects and criticality analyses (FMECA) describe the impact of identified faults. They form an important category of knowledge gathered during the design phase of a satellite and are used also for diagnosis activities. This paper proposes their extension, allowing a finer representation of the available knowledge, at approximately the same cost, through the introduction of an appropriate representation of uncertainty and incompleteness based on Zadeh's possibility theory and fuzzy sets. The main benefit of the approach is to provide a qualitative treatment of uncertainty where we can for instance distinguish manifestations which are more or less certainly present (or absent) and manifestations which are more or less possibly present (or absent) when a given fault is present. In a second step, the proposed approach is extended to handle fault impacts expressed as event chronologies. Efficient, real-time compatible discrimination techniques exploiting uncertain observations are introduced, and an example of satellite fault diagnosis illustrates the method. A brief rationale for the choice of possibility theory and fuzzy sets is provided.

A parametric model for fusing heterogeneous fuzzy data
R. J. Hathaway, J. C. Bezdek, W. Pedrycz
Dept. of Math. & Comput. Sci, Georgia Southern Univ., Statesboro, GA, USA
vol. 4, no. 3, pp. 270-81, Aug. 1996

Presented is a model that integrates three data types (numbers, intervals, and linguistic assessments). Data of these three types come from a variety of sensors. One objective of sensor-fusion models is to provide a common framework for data integration, processing, and interpretation. That is what our model does. We use a small set of artificial data to illustrate how problems as diverse as feature analysis, clustering, cluster validity, and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model. The effects of reparameterization on computational outputs are discussed. Numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types.

A reasoning algorithm for high-level fuzzy Petri nets
H. Scarpelli, F. Gomide, R. R. Yager
Univ. Federal de Sao Carlos, Brazil
vol. 4, no. 3, pp. 282-94, Aug. 1996

We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query.

Adaptive fuzzy rule-based classification systems
K. Nozaki, H. Ishibuchi, H. Tanaka
Dept. of Ind. Eng., Osaka Prefecture Univ., Japan
vol. 4, no. 3, pp. 238-50, Aug. 1996

This paper proposes an adaptive method to construct a fuzzy rule-based classification system with high performance for pattern classification problems. The proposed method consists of two procedures: an error correction-based learning procedure, and an additional learning procedure. The error correction-based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance. That is, when a pattern is misclassified by a particular fuzzy rule, the grade of certainty of that rule is decreased. On the contrary, when a pattern is correctly classified, the grade of certainty is increased. Because the error correction-based learning procedure is not meaningful after all the given patterns are correctly classified, we cannot adjust a classification boundary in such a case. To acquire a more intuitively acceptable boundary, we propose an additional learning procedure. We also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules, which consists of the error correction-based learning procedure and the concept of forgetting. We can construct a compact fuzzy rule-based classification system with high performance.

Continuous fuzzy conjunctions and disjunctions
J. Harmse
Anal. & Appl. es. Div., Tracor Appl. Sci., Austin, TX, USA
vol. 4, no. 3, pp. 295-314, Aug. 1996

Several functions have been used to implement conjunction and disjunction in fuzzy logic and to implement intersection and union in fuzzy set theory. Usually t-norms and t-conorms are used, but for some applications these may not be the best function classes. In this paper, I propose specific requirements which a function should satisfy if it is to be used to implement conjunction (or intersection) or disjunction (or union) and compare the functions proposed for conjunction to t-norms. In addition to stating basic properties of the resulting function classes, I give theorems on polynomial approximation within each class and on the existence of functions in either class with specified values at particular points.

A multirule-base controller using the robust property of a fuzzy controller and its design method
Kim Seungwoo, Cho Youngwan, Park Mignon
Dept. of Electron. Eng., Yonsei Univ., Seoul, South Korea
vol. 4, no. 3, pp. 315-27, Aug. 1996

This paper suggests a new fuzzy adaptive controller, which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a multirule-base architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. Here, we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. The performance of the proposed adaptive control algorithm is analyzed through a design example and a DC motor control simulation.

Hardware design of asynchronous fuzzy controllers
A Costa, A. De Gloria, M. Olivieri
DIBE, Genoa Univ., Italy
vol .4, no. 3, pp. 328-38, Aug. 1996

This paper presents a hardware approach to the design of fuzzy controllers which, by exploiting some peculiar characteristics of fuzzy logic computation, allows one to save power consumption and increase computing speed. We show that the computation involved in a fuzzy controller has some statistic features that can be exploited by asynchronous computation. This paper presents a quantitative study of the statistical properties of fuzzy computation. A design methodology is introduced, and two experimental applications are shown.

Stable adaptive control using fuzzy systems and neural networks
J. T. Spooner, K. M. Passino
Dept. of Electr. Eng., Ohio State Univ., Columbus, OH, USA
vol. 4, no. 3, pp. 339-59, Aug. 1996

Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics. The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller. We prove that with or without such knowledge both adaptive schemes can "learn" how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input. In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation. The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane.

Neuro-fuzzy hybrid control system of tank level in petroleum plant
T. Tani, S. Murakoshi, M. Umano
Manuf. Dept., Idemitsu Kosan Co. Ltd., Chiba, Japan
vol. 4, no. 3, pp. 360-8, Aug. 1996

Shown in this paper is a practical method of control using neural network and fuzzy control techniques, where a neural network estimates the target of fuzzy control. The neural network is used to estimate the transient state of a plant which has nonlinear processes such as refrigerating and filtering. The suitable control target pattern for fuzzy control is selected according to this estimation. This method is applied to control the tank level of a solvent dewaxing plant for: 1) changing the tank outflow rate smoothly, and 2) keeping the tank level stable. The results show that this system can control the tank level effectively in both steady state and transient state.

Evaluation of min/max instructions for fuzzy information processing
H. Watanabe, D. Chen, S. Konuri
Mercury Technol. Inc., New York, NY, USA
vol.4, no. 3. pp. 369-74. Aug. 1996

We report the results of dynamic measurements which evaluate the effectiveness of an application specific microprocessor for fuzzy control and fuzzy information processing. We propose to specialize an architecture of microprocessor for fuzzy theoretic operations using quantitative techniques developed by designers of reduced instruction set computer (RISC). In particular, an introduction of specialized instructions is considered. Experimental results show that we can achieve as high as 2.5 speed up of a program for fuzzy control by introducing two instructions-min and max.

On fuzzy associative memory with multiple-rule storage capacity
Lai Chung Fu, Lee Tong
Dept. of Comput., Hong Kong Polytech., Kowloon, Hong Kong
vol. 4, no. 3, pp. 375-84, Aug. 1996

Kosko's fuzzy associative memory (FAM) is the very first neural network model for implementing fuzzy systems. Despite its success in various applications, the model suffers from very low storage capacity, i.e., one rule per FAM matrix. A lot of hardware and computations are usually required to implement the model and, hence, it is limited to applications with small fuzzy rule-base. In this paper, the inherent property for storing multiple rules in a FAM matrix is identified. A theorem for perfect recalls of all the stored rules is established and based upon which the hardware and computation requirements of the FAM model can be reduced significantly. Furthermore, we have shown that when the FAM model is generalized to the one with max-bounded-product composition, single matrix implementation is possible if the rule-base is a set of semi-overlapped fuzzy rules. Rule modification schemes are also developed and the inference performance of the established high capacity models is reported through a numerical example.

The possibilistic C-means algorithm: insights and recommendations
R. Krishnapuram, J. M. Keller
Dept. of Comput. Eng. & Comput. Sci., Missouri Univ., Columbia, MO, USA
vol. 4, no. 3, pp. 385-93, Aug. 1996

Recently, the possibilistic C-means algorithm (PCM) was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy C-means (FCM). In this issue, Barni et al. (1996) report a difficulty they faced while applying the PCM, and note that it exhibits an undesirable tendency to converge to coincidental clusters. The purpose of this paper is not just to address the issues raised by Barni et al., but to go further and analytically examines the underlying principles of the PCM and the possibilistic approach, in general. We analyze the data sets used by Barni et al. and interpret the results reported by them in the light of our findings.

Comments on "A possibilistic approach to clustering"
M. Barni, V. Cappellini, A. Mecocci
Dept. of Electron. Eng., Florence Univ., Italy
vol. 4, no. 3, pp. 393-6, Aug. 1996.

In this comment, we report a difficulty with the-application of the possibilistic approach to fuzzy clustering (PCM) proposed by Keller and Krishnapuram (1993). In applying this algorithm we found that it has the undesirable tendency to produce coincidental clusters. Results illustrating this tendency are reported and a possible explanation for the PCM behavior is suggested.