Fuzzy-Systeme

1 As a treatise on fuzzy set theory and its applications, "Foundations of Fuzzy Systems," by R. Kruse, J. Gebhardt and F. Klawonn, has few equals. Succinct, authoritative and up-to-date, it covers the basic theory very thoroughly and precisely, with emphasis on those aspects of the theory which play an important role in its applications. This is especially true of the chapters dealing with the calculus of fuzzy if-then rules - a subset of fuzzy set theory which plays a central role in the applications relating to the conception and design of both control and knowledge-based systems. To view the contents of "Foundations of Fuzzy Systems" in a proper perspective, a digression is in order. First, it is important to recognize that any crisp theory X can be fuzzified and hence generalized to fuzzy X - by replacing the concept of a crisp set in X by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory.

Autorentext
Prof. Dr. Rudolf Kruse ist Leiter des Lehrstuhls für Neuro-Fuzzy-Systeme an der Universität Magdeburg. Prof. Dr. Frank Klawonn ist an der FH Braunschweig (Bereich Data Mining, Fuzzy-Systeme, neuronale Netze und evolutionäre Algorithmen) tätig.

Klappentext

1 As a treatise on fuzzy set theory and its applications, "Foundations of Fuzzy Systems," by R. Kruse, J. Gebhardt and F. Klawonn, has few equals. Succinct, authoritative and up-to-date, it covers the basic theory very thoroughly and precisely, with emphasis on those aspects of the theory which play an important role in its applications. This is especially true of the chapters dealing with the calculus of fuzzy if-then rules - a subset of fuzzy set theory which plays a central role in the applications relating to the conception and design of both control and knowledge-based systems. To view the contents of "Foundations of Fuzzy Systems" in a proper perspective, a digression is in order. First, it is important to recognize that any crisp theory X can be fuzzified and hence generalized to fuzzy X - by replacing the concept of a crisp set in X by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory.

Inhalt
1 Einleitung.- 1.1 Fuzzy-Systeme.- 1.2 Modellierung vager, impräziser und unsicherer Informationen.- 1.3 Zu diesem Buch.- 2 Grundlagen der Theorie der Fuzzy-Mengen.- 2.1 Fuzzy-Mengen: Eine motivierende Einführung.- 2.2 Einfache Repräsentationsformen für Fuzzy-Mengen.- 2.3 Verknüpfungen von Fuzzy-Mengen.- 2.4 Das Extensionsprinzip.- 2.5 Effizientes Operieren auf Fuzzy-Mengen.- 2.6 Zur Semantik von Fuzzy-Mengen.- 2.7 Fuzzy-Logik.- 2.8 Ergänzende Bemerkungen und Quellenangaben.- 3 Approximatives Schließen.- 3.1 Possibilitätsverteilungen und Unsicherheitsmaße.- 3.2 Konzeption eines Expertensystems für possibilistische Daten.- 3.3 Interpretation possibilistischer Inferenzregeln.- 3.4 Wissensrepräsentation und -propagation mit Hypergraphen.- 3.5 Logikbasierte Inferenzmechanismen.- 3.6 Ergänzende Bemerkungen und Quellenangaben.- 4 Fuzzy-Regelung.- 4.1 Kognitive versus klassische Modelle.- 4.2 Zwei Ansätze zur Fuzzy-Regelung.- 4.3 Entwurf und Optimierung von Fuzzy-Reglern.- 4.4 Fuzzy-Regelung auf der Basis von Gleichheitsrelationen.- 4.5 Fuzzy-Regelung und Relationalgleichungen.- 4.6 Ergänzende Bemerkungen und Quellenangaben.- Symbole.