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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
A new fuzzy bee colony optimization with dynamic adaptation of parameters using interval type-2 fuzzy logic for tuning fuzzy controllers
TL;DR: This paper considered different levels and types of noise in the simulations to analyze the approach of interval type-2 fuzzy logic systems to find the best values of alpha and beta for BCO when applied in the design of fuzzy controllers.
Journal ArticleDOI
Fuzzy criteria for feature selection
TL;DR: This paper proposes to use fuzzy criteria in feature selection by using a fuzzy decision making framework, which allows for a more flexible definition of the goals infeature selection, and avoids the problem of weighting different goals is classical multi-objective optimization.
Journal ArticleDOI
Antiforgery: a novel pseudo-outer product based fuzzy neural network driven signature verification system
Chai Quek,R. W. Zhou +1 more
TL;DR: A novel pseudo-outer product based fuzzy neural network (POPFNN-TVR) driven signature verification system called the antiforgery system is presented in this paper and its characteristics, such as the learning ability, generalization ability, and high computational ability, make ant iforgery particularly powerful when verifying skilled forgeries.
Journal ArticleDOI
Cluster analysis based on fuzzy equivalence relation
TL;DR: By utilizing this clustering analysis, the subjects' fuzzy assessments with various rating attitudes can be taken into account in the aggregation process to assure more convincing and accurate cluster analysis.
Journal ArticleDOI
Fuzzy numbers and fuzzification of the Choquet integral
TL;DR: The presented generalized Choquet integral with respect to signed fuzzy measure can act as an aggregation tool which is especially useful in many information fusing and data mining problems (such as regression and classification) where not only crisp data but also heterogeneous fuzzy data are involved.
References
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Journal ArticleDOI
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.
Journal ArticleDOI
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).
Journal ArticleDOI
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.