Open AccessBook
Fuzzy Sets and Fuzzy Logic: Theory and Applications
George J. Klir,Bo Yuan +1 more
Reads0
Chats0
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
More filters
ReportDOI
Constructing Probability Boxes and Dempster-Shafer Structures
TL;DR: A variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge are summarized.
Journal ArticleDOI
Memory effects in complex materials and nanoscale systems
TL;DR: The memory properties of various materials and systems which appear most strikingly in their non-trivial, time-dependent resistive, capacitative and inductive characteristics are described within the framework of memristors, memcapacitors and meminductors.
Journal ArticleDOI
A fuzzy AHP and BSC approach for evaluating performance of IT department in the manufacturing industry in Taiwan
TL;DR: An approach based on the fuzzy analytic hierarchy process (FAHP) and balanced scorecard (BSC) for evaluating an IT department in the manufacturing industry in Taiwan is constructed and is suggested to be a good tool for solving other multiple-criteria decision-making problems.
Book
Interval Neutrosophic Sets and Logic: Theory and Applications in Computing
TL;DR: This work defines the set-theoretic operators on an instance of a neutrosophic set, and calls it an Interval Neutrosophics Set (INS), and introduces a new logic system based on interval neutrosophile sets and proposed data model based on the extension of fuzzy data model and paraconsistent data model.
Journal ArticleDOI
Selecting among five common modelling approaches for integrated environmental assessment and management
R. A. Kelly,Anthony Jakeman,Olivier Barreteau,Mark E. Borsuk,Sondoss Elsawah,Serena H. Hamilton,Hans Jørgen Henriksen,Sakari Kuikka,Holger R. Maier,Andrea Emilio Rizzoli,Hedwig van Delden,Alexey Voinov +11 more
TL;DR: A guiding framework is presented that aims to assist modellers and model users in the choice of an appropriate modelling approach for their integrated assessment applications and that enables more effective learning in interdisciplinary settings.
References
More filters
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.