Analysis and control of fuzzy systems using finite discrete relations

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Abstract
This paper considers the difficulties which arise from an attempt to analyse fuzzy systems. Previous work in this area is briefly reviewed and a new way of describing closed-loop fuzzy systems is introduced. Using only finite discrete fuzzy relations, it is possible to define such concepts as state equivalence, stability and controllability, and, by restricting attention to a special class of systems, a simple control problem can be solved. The basic ideas discussed in the paper are, perhaps, the first steps towards a practical theory of fuzzy systems.

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