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Volume 1 (2006)

Advances in Fuzzy Sets and Systems

Advances in Fuzzy Sets and Systems
Volume 2, Issue 1, Pages 57 - 80 (February 2007)

PROPERTIES OF DISCRETE KNOWLEDGE SYSTEMS
Albert Kong (West Indies)

Abstract:
A discrete knowledge-processing paradigm is introduced that permits knowledge encoding and decoding precision to be traded with complexity. The result is the ability to decode very complex systems in real time. The encoding of knowledge may take some time depending on the precision desired and cannot or at least should not be expected to be as immediate as the decoding. The decoding time of course is critical. It is not acceptable for a user to wait a long time for an output given input (or a decoding of knowledge) from the model even if it is acceptable that the encoding may take a very long time. A less precise but timely result may be more appropriate than a perfectly precise result that comes too late. The means to this end, that is, the discrete knowledge-processing paradigm may turn out to be more useful than the end itself, as it has revealed new ways of analysis and characterization of knowledge. The properties of discrete knowledge systems that permits this, would be shown in some detail for both low order systems (simple systems) where an explicit graphical demonstration is possible and high order systems (complex systems) where some abstract visualization may be required. Nevertheless, the regression performed, which like conventional neuro-fuzzy techniques is a complex optimization algorithm, is easily visualized as a rearrangement of components within a high dimensional sparse array that produces a model-target data match along with the discovery of natural rules. The new ways of analysis and characterization of knowledge along with interesting and appropriate terminology is introduced and explained. The results shown form a limited set of experiments performed that support the new concepts introduced from a larger pool of results in a study that is ongoing, but which is hopefully sufficient for the reader to gain an understanding of the work done.

Keywords and phrases: extract, discrete knowledge, knowledge components, regularity, rule clusters.

Communicated by Mi-Hye Kim

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