Mathematical Principles Of Fuzzy Logic
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Mathematical Principles Of Fuzzy Logic
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Author : Vilém Novák
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Principles Of Fuzzy Logic written by Vilém Novák and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
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Author : Radim Belohlavek
language : en
Publisher: Oxford University Press
Release Date : 2017-05-03
Fuzzy Logic And Mathematics written by Radim Belohlavek and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-03 with Philosophy categories.
The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.
Mathematical Modeling Using Fuzzy Logic
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Author : Abhijit Pandit
language : en
Publisher: CRC Press
Release Date : 2021-05-19
Mathematical Modeling Using Fuzzy Logic written by Abhijit Pandit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Business & Economics categories.
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.
Mathematics Behind Fuzzy Logic
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Author : Esko Turunen
language : en
Publisher: Physica
Release Date : 1999-09-24
Mathematics Behind Fuzzy Logic written by Esko Turunen and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-24 with Business & Economics categories.
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.
Fuzzy Relational Systems
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Author : Radim Belohlávek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fuzzy Relational Systems written by Radim Belohlávek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Mathematical Logic In Asia Proceedings Of The 9th Asian Logic Conference
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Author : Sergei S Goncharov
language : en
Publisher: World Scientific
Release Date : 2006-10-23
Mathematical Logic In Asia Proceedings Of The 9th Asian Logic Conference written by Sergei S Goncharov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-23 with Science categories.
This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, Δ1-induction, completeness of Leśniewski's systems, and reduction calculus for the satisfiability problem are also discussed.The coverage includes the answer to Kanovei's question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories.
Mathematics In Computational Science And Engineering
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Author : Ramakant Bhardwaj
language : en
Publisher: John Wiley & Sons
Release Date : 2022-05-11
Mathematics In Computational Science And Engineering written by Ramakant Bhardwaj and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-11 with Mathematics categories.
MATHEMATICS IN COMPUTATIONAL SCIENCE AND ENGINEERING This groundbreaking new volume, written by industry experts, is a must-have for engineers, scientists, and students across all engineering disciplines working in mathematics and computational science who want to stay abreast with the most current and provocative new trends in the industry. Applied science and engineering is the application of fundamental concepts and knowledge to design, build and maintain a product or a process, which provides a solution to a problem and fulfills a need. This book contains advanced topics in computational techniques across all the major engineering disciplines for undergraduate, postgraduate, doctoral and postdoctoral students. This will also be found useful for professionals in an industrial setting. It covers the most recent trends and issues in computational techniques and methodologies for applied sciences and engineering, production planning, and manufacturing systems. More importantly, it explores the application of computational techniques and simulations through mathematics in the field of engineering and the sciences. Whether for the veteran engineer, scientist, student, or other industry professional, this volume is a must-have for any library. Useful across all engineering disciplines, it is a multifactional tool that can be put to use immediately in practical applications. This groundbreaking new volume: Includes detailed theory with illustrations Uses an algorithmic approach for a unique learning experience Presents a brief summary consisting of concepts and formulae Is pedagogically designed to make learning highly effective and productive Is comprised of peer-reviewed articles written by leading scholars, researchers and professors AUDIENCE: Engineers, scientists, students, researchers, and other professionals working in the field of computational science and mathematics across multiple disciplines
Mathematical Logic In Asia
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Author : Rod G. Downey
language : en
Publisher: World Scientific
Release Date : 2006
Mathematical Logic In Asia written by Rod G. Downey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, ?1-induction, completeness of Le?niewski's systems, and reduction calculus for the satisfiability problem are also discussed.The coverage includes the answer to Kanovei's question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories.
Lectures On Soft Computing And Fuzzy Logic
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Author : Antonio Di Nola
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-31
Lectures On Soft Computing And Fuzzy Logic written by Antonio Di Nola and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-31 with Computers categories.
The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.
Fuzzy Logic For Beginners
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Author : Masao Mukaidono
language : en
Publisher: World Scientific
Release Date : 2001
Fuzzy Logic For Beginners written by Masao Mukaidono and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
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.