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.
Reihe
Auflage
Softcover reprint of hardcover 1st ed. 2007
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 13 mm
Gewicht
ISBN-13
978-90-481-7554-3 (9789048175543)
DOI
10.1007/978-1-4020-6164-6
Schweitzer Klassifikation
Sets, Relations, And Functions.- Lattices.- L-Fuzzy Relations.- Categories Of Relations.- Categories Of L-Fuzzy Relations.- Fuzzy Controllers In Goguen Categories.
