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Mathematical Principles of Fuzzy Logic

Author : Vilém Novák

Publisher : Springer Science & Business Media

Page : 327 pages

File Size : 23,3 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461552176

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Book Description

Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.



Fuzzy Logic and Mathematics

Author : Radim Bělohlávek

Publisher : Oxford University Press

Page : 545 pages

File Size : 32,29 MB

Release : 2017

Category : Mathematics

ISBN : 0190200014

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Book Description

The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.



Mathematical Modeling using Fuzzy Logic

Author : Abhijit Pandit

Publisher : CRC Press

Page : 195 pages

File Size : 49,68 MB

Release : 2021-05-20

Category : Business & Economics

ISBN : 0429751710

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Book Description

Mathematical Modeling using Fuzzy Logic has been a dream project for the author. Fuzzy logic provides a unique method of approximate reasoning in an imperfect world. This text is a bridge to the principles of fuzzy logic through an application-focused approach to selected topics in engineering and management. The many examples point to the richer solutions obtained through fuzzy logic and to the possibilities of much wider applications. There are relatively very few texts available at present in fuzzy logic applications. The style and content of this text is complementary to those already available. New areas of application, like application of fuzzy logic in modeling of sustainability, are presented in a graded approach in which the underlying concepts are first described. The text is broadly divided into two parts: the first treats processes, materials, and system applications related to fuzzy logic, and the second delves into the modeling of sustainability with the help of fuzzy logic. This book offers comprehensive coverage of the most essential topics, including: Treating processes, materials, system applications related to fuzzy logic Highlighting new areas of application of fuzzy logic Identifying possibilities of much wider applications of fuzzy logic Modeling of sustainability with the help of fuzzy logic The level enables a selection of the text to be made for the substance of undergraduate-, graduate-, and postgraduate-level courses. There is also sufficient volume and quality for the basis of a postgraduate course. A more restricted and judicious selection can provide the material for a professional short course and various university-level courses.



Fuzzy Set Theory

Author : George J. Klir

Publisher :

Page : 264 pages

File Size : 50,3 MB

Release : 1997

Category : Computers

ISBN :

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Book Description

Fuzzy Set Theory: Foundations and Applications serves as a simple introduction to basic elements of fuzzy set theory. The emphasis is on a conceptual rather than a theoretical presentation of the material. Fuzzy Set Theory also contains an overview of the corresponding elements of classical set theory - including basic ideas of classical relations - as well as an overview of classical logic. Because the inclusion of background material in these classical foundations provides a self-contained course of study, students from many different academic backgrounds will have access to this important new theory.



Data Engineering

Author : Olaf Wolkenhauer

Publisher : John Wiley & Sons

Page : 296 pages

File Size : 23,42 MB

Release : 2004-04-07

Category : Technology & Engineering

ISBN : 0471464104

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Book Description

Although data engineering is a multi-disciplinary field withapplications in control, decision theory, and the emerging hot areaof bioinformatics, there are no books on the market that make thesubject accessible to non-experts. This book fills the gap in thefield, offering a clear, user-friendly introduction to the maintheoretical and practical tools for analyzing complex systems. Anftp site features the corresponding MATLAB and Mathematical toolsand simulations. Market: Researchers in data management, electrical engineering,computer science, and life sciences.



Fuzzy Relational Systems

Author : Radim Belohlávek

Publisher : Springer Science & Business Media

Page : 376 pages

File Size : 28,42 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461506336

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Book Description

Since their inception, fuzzy sets and fuzzy logic became popular. The reason is that the very idea of fuzzy sets and fuzzy logic attacks an old tradition in science, namely bivalent (black-or-white, all-or-none) judg ment and reasoning and the thus resulting approach to formation of scientific theories and models of reality. The idea of fuzzy logic, briefly speaking, is just the opposite of this tradition: instead of full truth and falsity, our judgment and reasoning also involve intermediate truth values. Application of this idea to various fields has become known under the term fuzzy approach (or graded truth approach). Both prac tice (many successful engineering applications) and theory (interesting nontrivial contributions and broad interest of mathematicians, logicians, and engineers) have proven the usefulness of fuzzy approach. One of the most successful areas of fuzzy methods is the application of fuzzy relational modeling. Fuzzy relations represent formal means for modeling of rather nontrivial phenomena (reasoning, decision, control, knowledge extraction, systems analysis and design, etc. ) in the pres ence of a particular kind of indeterminacy called vagueness. Models and methods based on fuzzy relations are often described by logical formulas (or by natural language statements that can be translated into logical formulas). Therefore, in order to approach these models and methods in an appropriate formal way, it is desirable to have a general theory of fuzzy relational systems with basic connections to (formal) language which enables us to describe relationships in these systems.



Fuzzy Logic for Beginners

Author : Masao Mukaidono

Publisher : World Scientific

Page : 117 pages

File Size : 12,71 MB

Release : 2001

Category : Computers

ISBN : 9810245343

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Book Description

There are many uncertainties in the real world. Fuzzy theory treats a kind of uncertainty called fuzziness, where it shows that the boundary of yes or no is ambiguous and appears in the meaning of words or is included in the subjunctives or recognition of human beings. Fuzzy theory is essential and is applicable to many systems -- from consumer products like washing machines or refrigerators to big systems like trains or subways. Recently, fuzzy theory has been a strong tool for combining new theories (called soft computing) such as genetic algorithms or neural networks to get knowledge from real data. This introductory book enables the reader to understand easily what fuzziness is and how one can apply fuzzy theory to real problems -- which explains why it was a best-seller in Japan.



Fuzzy Logic in Geology

Author : Robert V. Demicco

Publisher : Elsevier

Page : 374 pages

File Size : 38,48 MB

Release : 2003-10-20

Category : Computers

ISBN : 0080521894

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Book Description

What is fuzzy logic?--a system of concepts and methods for exploring modes of reasoning that are approximate rather than exact. While the engineering community has appreciated the advances in understanding using fuzzy logic for quite some time, fuzzy logic's impact in non-engineering disciplines is only now being recognized. The authors of Fuzzy Logic in Geology attend to this growing interest in the subject and introduce the use of fuzzy set theory in a style geoscientists can understand. This is followed by individual chapters on topics relevant to earth scientists: sediment modeling, fracture detection, reservoir characterization, clustering in geophysical data analysis, ground water movement, and time series analysis.George Klir is the Distinguished Professor of Systems Science and Director of the Center for Intelligent Systems, Fellow of the IEEE and IFSA, editor of nine volumes, editorial board member of 18 journals, and author or co-author of 16 booksForeword by the inventor of fuzzy logic-- Professor Lotfi Zadeh



Mathematics Behind Fuzzy Logic

Author : Esko Turunen

Publisher : Physica

Page : 212 pages

File Size : 10,85 MB

Release : 1999-09-24

Category : Business & Economics

ISBN :

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Book Description

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.



Neural and Fuzzy Logic Control of Drives and Power Systems

Author : Marcian Cirstea

Publisher : Newnes

Page : 416 pages

File Size : 48,5 MB

Release : 2002-10-08

Category : Education

ISBN : 9780750655583

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Book Description

*Introduces cutting-edge control systems to a wide readership of engineers and students *The first book on neuro-fuzzy control systems to take a practical, applications-based approach, backed up with worked examples and case studies *Learn to use VHDL in real-world applications Introducing cutting edge control systems through real-world applications Neural networks and fuzzy logic based systems offer a modern control solution to AC machines used in variable speed drives, enabling industry to save costs and increase efficiency by replacing expensive and high-maintenance DC motor systems. The use of fast micros has revolutionised the field with sensorless vector control and direct torque control. This book reflects recent research findings and acts as a useful guide to the new generation of control systems for a wide readership of advanced undergraduate and graduate students, as well as practising engineers. The authors guide readers quickly and concisely through the complex topics of neural networks, fuzzy logic, mathematical modelling of electrical machines, power systems control and VHDL design. Unlike the academic monographs that have previously been published on each of these subjects, this book combines them and is based round case studies of systems analysis, control strategies, design, simulation and implementation. The result is a guide to applied control systems design that will appeal equally to students and professional design engineers. The book can also be used as a unique VHDL design aid, based on real-world power engineering applications.