Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

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Fuzzy Set Theory - and Its Applications

Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty,
and Information—an earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy Logic
addresses practically every significant topic in the broad expanse of the union of fuzzy set theory
and fuzzy logic. To me Fuzzy Sets and Fuzzy Logic is a remarkable achievement; it covers its vast
territory with impeccable authority, deep insight and a meticulous attention to detail.
To view Fuzzy Sets and Fuzzy Logic in a proper perspective, it is necessary to clarify a point
of semantics which relates to the meanings of fuzzy sets and fuzzy logic.
A frequent source of misunderstanding fias to do with the interpretation of fuzzy logic. The
problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow
sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization
of classical multivalued logics. But in a wider sense, fuzzy logic, FL^ is almost synonymous
with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLW is much
broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different
from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is
usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLW
In Fuzzy Sets and Fuzzy Logic, fuzzy logic is interpreted in a sense that is close to FLW. However,
to avoid misunderstanding, the title refers to both fuzzy sets and fuzzy logic.
Underlying the organization of Fuzzy Sets and Fuzzy Logic is a fundamental fact, namely,
that any field X and any theory Y can be fuzzified by replacing the concept of a crisp set in X and Y
by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory, probability
theory and logic, fuzzification leads to fuzzy arithmetic, fuzzy topology, fuzzy graph theory,
fuzzy probability theory and FLn. Similarly, hi application to applied fields such as neural network
theory, stability theory, pattern recognition and mathematical programming, fuzzification leads to
fuzzy neural network theory, fuzzy stability theory, fuzzy pattern recognition and fuzzy mathematical
programming. What is gained through fuzzification is greater generality, higher expressive
power, an enhanced ability to model real-world problems and, most importantly, a methodology for
exploiting the tolerance for imprecision—a methodology which serves to achieve tractability,

Fuzzy Sets and Fuzzy Logic: Theory and Applications

For pt.I see ibid., vol.20, no.2, p.404-18, 1990. The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined. Several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated. Defuzzification strategies, are discussed. Some of the representative applications of the FLC, from laboratory level to industrial process control, are briefly reported. Some unsolved problems are described, and further challenges in this field are discussed. >

Fuzzy logic in control systems: fuzzy logic controller. II

During the past several years, fuzzy control has emerged as one of the most active and fruitful areas for research in the applications of fuzzy set theory. Fuzzy control is based on fuzzy logic. The fuzzy logic controller (FLC) based on fuzzy logic provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy. A survey of the FLC is presented; a general methodology for constructing an FLC and assessing its performance is described; and problems that need further research are pointed out

Fuzzy logic in control systems : fuzzy logic controller. Part II

Fuzzy programming and linear programming with several objective functions

Der Begriff des Graphen sowie graphentheoretische Verfahren finden im Bereich des Operations Research verbreitet Anwendung. Spezielle Formen von Graphen — Baume — haben wir schon bei den Entscheidungsbaumverfahren kennengelernt, ohne dass dafur Kenntnisse in der Graphentheorie notwendig waren. Nutzlich sind solche Kenntnisse allerdings auf anderen Gebieten, so z.B. bei der Verwendung sogenannter Gozintographen in der Fertigungssteuerung und -planung und in der Netzplantechnik. Deshalb sollen im folgenden die fur das OR wichtigsten Grundlagen der Graphentheorie dargestellt werden. Fur ein tiefergehendes Studium sei auf die Spezialliteratur verwiesen (z.B. Neumann, 1975b; Noltemeier, 1976b; Sachs, 1971).

Graphen, Bäume, Netze, Netzpläne

Die Theorie der Unscharfen Mengen wird als ein neues Konzept vorgestellt, das fur die Formulierung und Losung von Systemen und Entscheidungsproblemen ein vielversprechendes Hilfsmittel zu sein und zu werden scheint. Nach einer kurzen Darstellung des bestehenden axiomatischen Systems werden einige potentielle Anwendungen beschrieben. Kritische Bemerkungen bezuglich des bisher bestehenden axiomatischen Systems und Andeutungen zu notwendigen zukunftigen Forschungsrichtungen beschliesen diesen einfuhrenden Aufsatz.

Hans-Jürgen Zimmermann

Papers

Graphen, Bäume, Netze, Netzpläne

Analyse, Beschreibung und Optimierung von unscharf formulierten Problemen.