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A VLSI fuzzy inference processor based on a discrete analog approach
V. Catania, A. Puliafito, M. Russo, L. Vita
vol. 2, no. 2, pp. 93-106, May 1994

In this paper we present a design for a general-purpose fuzzy processor, the core of which is based on an analog-numerical approach combining the inherent advantages of analog and digital implementations, above all as regards noise margins. The architectural model proposed was chosen in such a way as to obtain a processor capable of working with a considerable degree of parallelism. The internal structure of the processor is organized as a cascade of pipeline stages which perform parallel execution of the processes into which each inference can be decomposed. A particular feature of the project is the definition of a 'fuzzy-gate', which executes elementary fuzzy computations, on which construction of the whole core of the processor is based. Designed using CMOS technology, the core can be integrated into a single chip and can easily be extended. The performance obtainable, in the order of 50 Mega fuzzy rules per second, is of a considerable level.

Measuring fuzzy uncertainty
N. R. Pal, J. C. Bezdek
vol. 2, no. 2, pp. 107-18, May 1994

First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Some relationships between several existing and the new measures are established, and some new properties are derived. The relative merits and drawbacks of different measures for applications are discussed. A weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced. Finally, we comment on the construction of measures that may assess all of the uncertainties associated with a physical system.

A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer
K. Tanaka, M. Sano
vol. 2, no. 2, pp. 119-34, May 1994

A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions.

Fuzzy reasoning supported by Petri nets
A. J. Bugarin, S. Barro
vol. 2, no. 2, pp. 135-50, May 1994

We develop a representational model for the knowledge base (KB) of fuzzy production systems with rule chaining based on the Petri net formalism. The model presents the execution of a KB following a data driven strategy based on the sup-min compositional rule of inference. In this connection, algorithms characterizing different situations have been described, including the case where the KB is characterized by complete information about all the input variables and the case where it is characterized by ignorance of some of these variables. For this last situation we develop a process of "incremental reasoning"; this process allows the KB to take information about previously unknown values into consideration as soon as such information becomes available. Furthermore, as compared to other solutions, the rule chaining mechanism we introduce is more flexible, and the description of the rules more generic. The computational complexity of these algorithms is O((C/2+M+N)R/sup 2/) for the "complete information" case and O((M+N)R/sup 2/) and O(2(M+N)R/sup 2/) for the other cases, where R is the number of fuzzy conditional statements of the KB, M and N the maximum number of antecedents and consequents in the rules and C the number of chaining transitions in the KB representation.

OR/AND Neuron in Modeling Fuzzy Set Connectives
K. Hirota, W. Pedrycz
vol. 2, no. 2, pp. 151-61, May 1994

The paper introduces a neural network-based model of logical connectives. neurons structured into a three layer topology. Due to the functional within its supervised learning. Further analysis of the connections of the neuron obtained in this way provides a better insight into the nature of the connectives applied in fuzzy sets by emphasizing their features of "locality" and interactivity. Afterward, we will study several architectures of neural networks comprising these neurons treated as their basic functional components. The numerical studies embrace both logical connectives (including the Zimmermann-Zysno data set, 1980) and the networks representing various decision-making architectures. We will neurons play an ultimate role.

Approximation theory of fuzzy systems-SISO case
Jun Zeng Xiao, M. G. Singh
UK
vol. 2, no. 2, pp. 162-76, May 1994. 1994

In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basic functions (FBF's), we first give a systematic and detailed analysis of FBF's and present five properties of FBF's: structure similarity and compatibility between the membership functions and FBF's, complementarity and less fuzziness of FBF's, and composition of fuzzy systems. These properties provide a clear picture of the shape and features of FBF's. Based on these properties of FBF's, we obtain some basic approximation properties of fuzzy systems: basic approximation property, uniform approximation property, uniform convergent property and universal approximation property. These results reveal the basic approximation mechanism of fuzzy systems and verify a few basic ideas in the design of fuzzy systems.

An inference network for bidirectional approximate reasoning based on an equality measure
Bien Zeungnam, Geun Chun Myung
Korea
vol. 2, no. 2, pp. 177-80, May 1994

An inference network is proposed as a tool for bidirectional approximate reasoning. The inference network can be designed directly from the given fuzzy data (knowledge). If a fuzzy input is given for the inference network, then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure. Conversely, due to the bidirectional structure, the network can yield its corresponding reasonable fuzzy input for a given fuzzy output. This property makes it possible to perform forward and backward reasoning in the knowledge base system.