Fuzzy Logic: Intelligence, Control, and Information
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1. Introduction. 2. Basic Concepts of Fuzzy Logic. 3. Fuzzy Sets. 4. Fuzzy Relations, Fuzzy Graphs, and Fuzzy Arithmetic. 5. Fuzzy If-Then Rules. 6. Fuzzy Implications and Approximate Reasoning. 7. Fuzzy Logic and Probability Theory. 8. Fuzzy Logic in Control Engineering. 9. Hierarchical Intelligent Control. 10. Analytical Issues in Fuzzy Logic Control. 11. Fuzzy Logic and Artificial Intelligence. 12. Fuzzy Logic in Database Management and Information Systems. 13. Fuzzy Logic in Pattern Recognition. 14. Fuzzy Model Identification. 15.Advanced Topics of Fuzzy Model Identification. 16.Neuro-Fuzzy Systems. 17. Genetic Algorithms and Fuzzy Logic. References. Index.Keywords:
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Fuzzy electronics
Fuzzy Control Language
Fuzzy associative matrix
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This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required.
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Included in Prentice Hall's MATLAB Curriculum Series, this text provides a comprehensive treatment of the methodologies underlying neuro-fuzzy and soft computing. The book places equal emphasis on theoretical aspects of covered methodologies, empirical observations, and verifications of various applications in practice.
Soft Computing
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A fuzzy logic system (FLS) is unique in that it is able to simultaneously handle numerical data and linguistic knowledge. It is a nonlinear mapping of an input data (feature) vector into a scalar output, i.e., it maps numbers into numbers. Fuzzy set theory and fuzzy logic establish the specifics of the nonlinear mapping. This tutorial paper provides a guided tour through those aspects of fuzzy sets and fuzzy logic that are necessary to synthesize an FLS. It does this by starting with crisp set theory and dual logic and demonstrating how both can be extended to their fuzzy counterparts. Because engineering systems are, for the most part, causal, we impose causality as a constraint on the development of the FLS. After synthesizing a FLS, we demonstrate that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks. The fuzzy basis function expansion is very powerful because its basis functions can be derived from either numerical data or linguistic knowledge, both of which can be cast into the forms of IF-THEN rules.< >
Fuzzy associative matrix
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Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called adaptive-network-based fuzzy inference system (ANFIS), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.< >
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About the Author. Preface to the Third Edition. 1 Introduction. The Case for Imprecision. A Historical Perspective. The Utility of Fuzzy Systems. Limitations of Fuzzy Systems. The Illusion: Ignoring Uncertainty and Accuracy. Uncertainty and Information. The Unknown. Fuzzy Sets and Membership. Chance Versus Fuzziness. Sets as Points in Hypercubes. Summary. References. Problems. 2 Classical Sets and Fuzzy Sets. Classical Sets. Operations on Classical Sets. Properties of Classical (Crisp) Sets. Mapping of Classical Sets to Functions. Fuzzy Sets. Fuzzy Set Operations. Properties of Fuzzy Sets. Alternative Fuzzy Set Operations. Summary. References. Problems. 3 Classical Relations and Fuzzy Relations. Cartesian Product. Crisp Relations. Cardinality of Crisp Relations. Operations on Crisp Relations. Properties of Crisp Relations. Composition. Fuzzy Relations. Cardinality of Fuzzy Relations. Operations on Fuzzy Relations. Properties of Fuzzy Relations. Fuzzy Cartesian Product and Composition. Tolerance and Equivalence Relations. Crisp Equivalence Relation. Crisp Tolerance Relation. Fuzzy Tolerance and Equivalence Relations. Value Assignments. Cosine Amplitude. Max Min Method. Other Similarity Methods. Other Forms of the Composition Operation. Summary. References. Problems. 4 Properties of Membership Functions, Fuzzification, and Defuzzification. Features of the Membership Function. Various Forms. Fuzzification. Defuzzification to Crisp Sets. -Cuts for Fuzzy Relations. Defuzzification to Scalars. Summary. References. Problems. 5 Logic and Fuzzy Systems. Part I Logic. Classical Logic. Proof. Fuzzy Logic. Approximate Reasoning. Other Forms of the Implication Operation. Part II Fuzzy Systems. Natural Language. Linguistic Hedges. Fuzzy (Rule-Based) Systems. Graphical Techniques of Inference. Summary. References. Problems. 6 Development of Membership Functions. Membership Value Assignments. Intuition. Inference. Rank Ordering. Neural Networks. Genetic Algorithms. Inductive Reasoning. Summary. References. Problems. 7 Automated Methods for Fuzzy Systems. Definitions. Batch Least Squares Algorithm. Recursive Least Squares Algorithm. Gradient Method. Clustering Method. Learning From Examples. Modified Learning From Examples. Summary. References. Problems. 8 Fuzzy Systems Simulation. Fuzzy Relational Equations. Nonlinear Simulation Using Fuzzy Systems. Fuzzy Associative Memories (FAMS). Summary. References. Problems. 9 Decision Making with Fuzzy Information. Fuzzy Synthetic Evaluation. Fuzzy Ordering. Nontransitive Ranking. Preference and Consensus. Multiobjective Decision Making. Fuzzy Bayesian Decision Method. Decision Making Under Fuzzy States and Fuzzy Actions. Summary. References. Problems. 10 Fuzzy Classification. Classification by Equivalence Relations. Crisp Relations. Fuzzy Relations. Cluster Analysis. Cluster Validity. c-Means Clustering. Hard c-Means (HCM). Fuzzy c-Means (FCM). Fuzzy c-Means Algorithm. Classification Metric. Hardening the Fuzzy c-Partition. Similarity Relations from Clustering. Summary. References. Problems. 11 Fuzzy Pattern Recognition. Feature Analysis. Partitions of the Feature Space. Single-Sample Identification. Multifeature Pattern Recognition. Image Processing. Summary. References. Problems. 12 Fuzzy Arithmetic and the Extension Principle. Extension Principle. Crisp Functions, Mapping, and Relations. Functions of Fuzzy Sets Extension Principle. Fuzzy Transform (Mapping). Practical Considerations. Fuzzy Arithmetic. Interval Analysis in Arithmetic. Approximate Methods of Extension. Vertex Method. DSW Algorithm. Restricted DSW Algorithm. Comparisons. Summary. References. Problems. 13 Fuzzy Control Systems. Control System Design Problem. Control (Decision) Surface. Assumptions in a Fuzzy Control System Design. Simple Fuzzy Logic Controllers. Examples of Fuzzy Control System Design. Aircraft Landing Control Problem. Fuzzy Engineering Process Control. Classical Feedback Control. Fuzzy Control. Fuzzy Statistical Process Control. Measurement Data Traditional SPC. Attribute Data Traditional SPC. Industrial Applications. Summary. References. Problems. 14 Miscellaneous Topics. Fuzzy Optimization. One-Dimensional Optimization. Fuzzy Cognitive Mapping. Concept Variables and Causal Relations. Fuzzy Cognitive Maps. Agent-Based Models. Summary. References. Problems. 15 Monotone Measures: Belief, Plausibility, Probability, and Possibility. Monotone Measures. Belief and Plausibility. Evidence Theory. Probability Measures. Possibility and Necessity Measures. Possibility Distributions as Fuzzy Sets. Possibility Distributions Derived from Empirical Intervals. Deriving Possibility Distributions from Overlapping Intervals. Redistributing Weight from Nonconsonant to Consonant Intervals. Comparison of Possibility Theory and Probability Theory. Summary. References. Problems. Index.
Defuzzification
Fuzzy Mathematics
Fuzzy associative matrix
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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,
Defuzzification
Fuzzy Control Language
T-norm fuzzy logics
Fuzzy associative matrix
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