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Fuzzy machines in a category

Published online by Cambridge University Press:  17 April 2009

Michael A. Arbib  and
Ernest G. Manes
Michael A. Arbib
Affiliation:
Department of Computer and Information Science, University of Massachusetts, Amherst, Massachusetts, USA
Ernest G. Manes
Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts, USA.
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Abstract

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“Fuzzy theories” and “distributive laws” are used to define “fuzzy systems” in an arbitrary category. The resulting minimal realization theory provides new insights even in classical cases (so that, for non-deterministic sequential machines, the minimal realization problem is reformulated in terms of the structure of join-irreducibles in finite lattices). The definition of “fuzzy theory” is of independent interest and meshes well with philosophical aspects of fuzzy set theory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 2 , October 1975 , pp. 169 - 210
Copyright
Copyright © Australian Mathematical Society 1975

References

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