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.

https://www.springer.com/productFlyer_978-0-7923-7435-0.pdf?SGWID=0-0-1297-33300503-0

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

Classical Sets and Fuzzy Sets.- Classical and Fuzzy Relations.- Membership Functions.- Defuzzification.- Fuzzy Rule-Based System.- Fuzzy Decision Making.- Applications of Fuzzy Logic.- Fuzzy Logic Projects with Matlab.

Introduction to Fuzzy Logic using MATLAB

This paper surveys expert systems (ES) development using a literature review and classification of articles from 1995 to 2004 with a keyword index and article abstract in order to explore how ES methodologies and applications have developed during this period. Based on the scope of 166 articles from 78 academic journals (retrieved from five online database) of ES applications, this paper surveys and classifies ES methodologies using the following eleven categories: rule-based systems, knowledge-based systems, neural networks, fuzzy ESs, object-oriented methodology, case-based reasoning, system architecture, intelligent agent systems, database methodology, modeling, and ontology together with their applications for different research and problem domains. Discussion is presented, indicating the followings future development directions for ES methodologies and applications: (1) ES methodologies are tending to develop towards expertise orientation and ES applications development is a problem-oriented domain. (2) It is suggested that different social science methodologies, such as psychology, cognitive science, and human behavior could implement ES as another kind of methodology. (3) The ability to continually change and obtain new understanding is the driving power of ES methodologies, and should be the ES application of future works.

http://www.sci.brooklyn.cuny.edu/~kopec/cis718/fall_2005/sdarticle5.pdf

Expert system methodologies and applications—a decade review from 1995 to 2004

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Fuzzy set theory has a number of properties that make it suitable for formalizing the uncertain information upon which medical diagnosis and treatment is usually based. Firstly, it defines inexact medical entities as fuzzy sets. Secondly, it provides a linguistic approach with an excellent approximation to texts. Finally, fuzzy logic offers reasoning methods capable of drawing approximate inferences. These facts suggest that fuzzy set theory might be a suitable basis for the development of a computerized diagnosis system. This is verified by trials performed with the medical expert system CADIAG-2, which uses fuzzy set theory to formalize medical relationships and fuzzy logic to model the diagnostic process.

Fuzzy Set Theory in Medical Diagnosis

https://publik.tuwien.ac.at/files/PubDat_213929.pdf

The Arden Syntax standard for clinical decision support

A model of a computer-assisted diagnostic system using fuzzy subsets has been developed. The physician documents symptom-diagnosis presence relationships and symptom-diagnosis conclusiveness relationships by means of labels of the fuzzy subsets never, almost nevm·, very very seldom, very seldom, seldom, m01·e or less seldom, not known, more 01· less often, often, very often, ve1·y ve1·y often, almost always, always. Symptoms are regarded as fuzzy subsets of reference sets. The reference set includes all values the symptom may assume. The degree of membership of a value in the fuzzy subset of a symptom is calculated when the patient's symptom pattern is available. By means of compositions of fuzzy relations, four different diagnostic indications are determined for every diagnosis under consideration: presence indication, conclusiveness indication, non-p1·esence indication and non-symptom presence indication. By performing the diagnostic process, the system provides the physician with proven diagnoses, excl~tded diagnoses and diagnostic hints, including reasons for the diagnoses displayed. Proposals for further investigations may also be requested.

A fuzzy logical model of computer-assisted medical diagnosis.

https://www.meduniwien.ac.at/kpa/publications/2004_AIIM_--_Knowledge_Acquisition_in_the_Fuzzy_Knowledge_Representation_Framework.pdf

Knowledge acquisition in the fuzzy knowledge representation framework of a medical consultation system

http://www.meduniwien.ac.at/kpa/publications/1994_FSAS_--_Clinical_Monitoring_with_Fuzzy_Automata.pdf

Klaus-Peter Adlassnig

Papers

Fuzzy Set Theory in Medical Diagnosis

The Arden Syntax standard for clinical decision support

A fuzzy logical model of computer-assisted medical diagnosis.

Knowledge acquisition in the fuzzy knowledge representation framework of a medical consultation system

Clinical monitoring with fuzzy automata