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Self-reference and chaos in fuzzy logic
P. Grim
vol. 1, no. 4, pp. 237-53, Nov. 1993

Investigates a range of phenomena from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the (0,1) interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and in three dimensions in the graphing of mutually referential triples.

Fuzzy-set based models of neurons and knowledge-based networks
W. Pedrycz, A. F. Rocha
vol. 1, no. 4, pp. 254-66, Nov. 1993

We will introduce and study different fuzzy-set oriented computational models of neurons. The generic topologies of the neurons emerging there encountered in the theory of fuzzy sets. The logical flavor of the proposed constructs is expressed in terms of operators used in their formalization and a way of their superposition in the neurons. The two and OR neurons) and referential processing units (such as matching, dominance, inclusion neurons). The specific features of the neurons are flexibly modeled with the aid of triangular norms. The inhibitory and excitatory characteristics are captured by embodying direct and complemented (negated) input signals. We will propose various topologies of neural networks put together with the use of these neurons and demonstrate straightforward relationships coming off between the problem specificity and the resulting architecture of the network. This limpid way of mapping the domain knowledge onto the structure of the network contributes significantly toward enhancements in learning processes in the network and substantially facilitates its interpretation.

Stability and control of fuzzy dynamic systems via cell-state transitions in fuzzy hypercubes
Kang Hoon
vol. 1, no. 4, pp. 267-79, Nov. 1993

The objective of this paper is to provide fuzzy control designers with a generalized design tool for stable fuzzy logic controllers in an optimal sense. Given multiple sets of data disturbed by vagueness uncertainty, we generate the implicative rules that guarantee stability and robustness of closed-loop fuzzy dynamic systems. First, the mathematical basis of fuzzy hypercubes and fuzzy dynamic systems is rigorously studied by considering the membership conditions for perfect recall and the evidential combination for reliable reasoning. Second, the author suggests the cell-state transition method, which utilizes Hsu's cell-to-cell mapping concept. As a result, a generic and implementable design methodology for obtaining a fuzzy feedback gain K, a fuzzy hypercube, is provided and illustrated with simple examples. The designed rules or membership functions in K form the cell-state transitions that lead an initial state to the goal state globally. The cell-state transition approach provides flexibility in choosing different controller rule bases depending on optimal strategies.

Learning control using fuzzified self-organizing radial basis function network
J. Nie, D. A. Linkens
vol. 1, no. 4, pp. 280-7, Nov. 1993

This note describes an approach to integrating fuzzy reasoning systems with radial basis function (RBF) networks and shows how the integrated network can be employed as a multivariable self-organizing and self-learning fuzzy controller. In particular, by drawing some equivalence between a simplified fuzzy control algorithm (SFCA) and a RBF network, we conclude that the RBF network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks, referred to as FBFN, with a variety of basis functions (not necessarily globally radial) synthesized from each dimension by fuzzy logical operators. On the other hand, as a result of natural generalization from RBF to SFCA, we claim that the fuzzy system like RBF is capable of universal approximation. Next, the FBFN is used as a multivariable rule-based controller but with an assumption that no rule-base exists, leading to a challenging problem of how to construct such a rule-base directly from the control environment. We propose a simple and systematic approach to performing this task by using a fuzzified competitive self-organizing scheme and incorporating an iterative learning control algorithm into the system. We have applied the approach to a problem of multivariable blood pressure control with a FBFN-based controller having six inputs and two outputs, representing a complicated control structure.

The fidelity of fuzzy-logic inference
K. K. Thornber
vol. 1, no. 4, pp. 288-97, Nov. 1993

The concept of fidelity of inference is introduced in order to quantify the degree to which the inferred value of a consequent can be regarded as valid. This concept also enhances our understanding of other aspects of fuzzy-logic inference including transitivity, intuitive leap, rada, and coupled implicative equations. It also enables many of the results derived earlier for element-by-element implication and derived implication to be taken over to inclusion and derived inclusion. Finally, it permits this inference to be carried out in hardware using simple circuitry, and provides a natural measure of noise immunity.

On methods for improving performance of PI-type fuzzy logic controllers
Lee Jihong
Korea
vol. 1, no. 4, pp. 298-301, Nov. 1993

To improve limitations of fuzzy PI controller especially when applied to high order systems, we propose two types of fuzzy logic controllers that take out appropriate amounts of accumulated control input according to fuzzily described situations in addition to the incremental control input calculated by conventional fuzzy PI controllers. The structures of the proposed controller were motivated by the problems of fuzzy PI controllers that they generally give inevitable overshoot when one tries to reduce rise time of response especially when a system of order higher than one is under consideration. Since the undesirable characteristics of the fuzzy PI controller are caused by integrating operation of the controller, even though the integrator itself is introduced to to overcome steady state error in response, we propose two fuzzy controllers that fuzzily clear out integrated quantities according to situation. The first controller determines the fuzzy resetting rate by situations described fuzzily by error and error rate, and the second one by error and control input. The two structures both give reduced rise time as well as small overshoot.