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Fuzzy Sets and Fuzzy Logic: Theory and Applications
George J. Klir,Bo Yuan +1 more
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TLDR
Fuzzy Sets and Fuzzy Logic is a true magnum opus; it addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic.Abstract:
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,read more
Citations
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Journal ArticleDOI
Polymer selection for SAW sensor array based electronic noses by fuzzy c-means clustering of partition coefficients: Model studies on detection of freshness and spoilage of milk and fish
Prabha Verma,R. D. S. Yadava +1 more
TL;DR: It is suggested that the present FCM method of polymer selection prior to sensor fabrication could be helpful in optimizing performance and reducing cost of SAW electronic noses for various applications.
Journal ArticleDOI
Fast factorization by similarity in formal concept analysis of data with fuzzy attributes
TL;DR: A fuzzy closure operator is described the fixed points of which are just clusters which uniquely determine the blocks of clusters of the factor lattice that represents an approximate version of the original concept lattice.
Journal ArticleDOI
An extension of the relational data model to incorporate ordered domains
TL;DR: The proposed model explores an important area of object-relational databases, since ordered domains can be viewed as a general kind of data type and justifies the development of Ordered SQL (OSQL) as a query language for ordered databases.
Journal ArticleDOI
Utilizing fuzzy compatibility of skill sets for team selection in multi-phase projects
TL;DR: A model is developed for the selection of personnel for a multiple phase project which takes into account the match between the skills possessed by each individual, the skills needed for each phase, and rather flexible budget considerations.
Journal ArticleDOI
A Fuzzy Logic-Based Prediction Model for Kerf Width in Laser Beam Machining
Anamul Hossain,Altab Hossain,Yusoff Nukman,Mohamed Hassan,M. Z. Harizam,A. M. Sifullah,Pedram Parandoush +6 more
TL;DR: In this paper, an intelligent fuzzy expert system (FES) model was used to predict the kerf width in CO2 laser cutting, where the employed input parameters were assisting gas pressure, laser power, cutting speed, and standoff distance.
References
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Fuzzy Set Theory in Medical Diagnosis
TL;DR: 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, and trials performed with the medical expert system CADIAG-2 suggest that it might be a suitable basis for the development of a computerized diagnosis system.
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On Some Logical Connectives for Fuzzy Sets Theory
TL;DR: In this paper, it was proved that distributivity, monotonicity and boundary conditions are essential assumptions for truth-functional logical connectives for fuzzy sets, under reasonable hypotheses (especially distributivity).
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Fuzzy decision trees
TL;DR: The decision trees method is extended to the case when the involved data appear as words belonging to the common language whose semantic representations are fuzzy sets, and a reformalization of the basic concepts of probability and utility theory is carried out.
Journal ArticleDOI
Design of a fuzzy controller using input and output mapping factors
TL;DR: A complete design procedure for a fuzzy three-term PID controller containing the rules along with the quantization and tuning procedures by means of input and output mapping factors is presented.