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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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Fuzzy Decision Tree Approach for Embedding Risk Assessment Information into Software Cost Estimation Model
TL;DR: A fuzzy decision tree approach for embedding risk assessment information into a software cost estimation model and shows that this model reveals the risk assessment of the generated software cost estimate, and at the same time yields an even more accurate result as compared to the original COCOMO model.
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Strict Archimedean t-norms and t-conorms as universal approximators
TL;DR: This paper shows that every continuous t -norm and t -conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm ( t - Conorm).
Journal ArticleDOI
Computing With Comparative Linguistic Expressions and Symbolic Translation for Decision Making: ELICIT Information
TL;DR: A new fuzzy linguistic representation model for comparative linguistic expressions is presented that takes advantage of the goodness of the 2-tuple linguistic representations model and improves the interpretability and accuracy of the results in computing with words processes, resulting the so-called extended comparative linguistic expression with symbolic translation.
Journal ArticleDOI
Modeling and Processing Measurement Uncertainty Within the Theory of Evidence: Mathematics of Random–Fuzzy Variables
TL;DR: The proposed approach yields to process measurement algorithms directly in terms of RFVs so that the final measurement result (and all associated available information) is provided as an RFV.
Journal ArticleDOI
On the relation between fuzzy max-Archimedean t-norm relational equations and the covering problem
TL;DR: This work extends Markovskii's work to fuzzy relational equations with max-Archimedean t-norm composition, and proves that there is a one-to-one correspondence between the minimal solutions of the equations and the irredundant coverings.
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.
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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.