Goguen categories extend the relational calculus and its
categorical formalization to the fuzzy world. Starting from the
fundamental concepts of sets, binary relations and lattices this
book introduces several categorical formulations of an abstract
theory of relations such as allegories, Dedekind categories and
related structures. It is shown that neither theory is sufficiently
rich to describe basic operations on fuzzy relations. The book then
introduces Goguen categories and provides a comprehensive study of
these structures including their representation theory, and the
definability of norm-based operations. The power of the theory is
demonstrated by a comprehensive example. A certain Goguen category
is used to specify and to develop a fuzzy controller. Based on its
abstract description as well as certain desirable properties and
their formal proofs, a verified controller is derived without
compromising the - sometimes - intuitive choice of norm-based
operations by fuzzy engineers.
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