Many concepts of problem solving theory are better understood in an abstract algebraic framework which also applies in automata theory. Because many systems of practical interest fall outside the scope of linear theory, it is desirable to enlarge as much as possible the class of systems for which a complete structure theory is available. The fuzzy system approach is presented as a basis for the design of systems far superior in artificial intelligence to those we can conceive today. The concepts of controllability, observability and minimality are developed, and conditions for the realization of an input‐output map by such a system are given. Several problems, all directly or indirectly related to fuzzification, arise in considering this broader class of systems.
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