Search Results: matrix-logic-theory-and-applications

Matrix Logic

Theory and Applications

Author: A. Stern

Publisher: Elsevier

ISBN: 1483295494

Category: Mathematics

Page: 220

View: 1835

In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base. The new formalism allows the author to enlarge the alphabet of the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole. As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense. Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers.

Fuzzy Logic Theory and Applications

Part I and Part II

Author: Lotfi A Zadeh,Rafik A Aliev

Publisher: World Scientific Publishing

ISBN: 9813238194

Category: Computers

Page: 612

View: 8686

Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications. Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples. This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.

Type-2 Fuzzy Logic: Theory and Applications

Author: Oscar Castillo,Patricia Melin

Publisher: Springer

ISBN: 3540762841

Category: Mathematics

Page: 244

View: 1535

This book describes new methods for building intelligent systems using type-2 fuzzy logic and soft computing (SC) techniques. The authors extend the use of fuzzy logic to a higher order, which is called type-2 fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we can build powerful hybrid intelligent systems that can use the advantages that each technique offers. This book is intended to be a major reference tool and can be used as a textbook.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author: Melvin Fitting,Ewa Orlowska

Publisher: Springer Science & Business Media

ISBN: 9783790815412

Category: Mathematics

Page: 374

View: 4656

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

An Introduction to Semi-tensor Product of Matrices and Its Applications

Author: Daizhan Cheng,Hongsheng Qi,Yin Zhao

Publisher: World Scientific

ISBN: 9814374687

Category: Mathematics

Page: 587

View: 8848

Proposes a generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP). This book offers a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.

Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices

Author: Adak, Amal Kumar,Manna, Debashree,Bhowmik, Monoranjan

Publisher: IGI Global

ISBN: 1522509151

Category: Computers

Page: 375

View: 9485

The use of fuzzy logic has become prominent in a variety of fields and applications. By implementing these logic sets, problems and uncertainties are more effectively resolved. Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices is a pivotal reference source for the latest scholarly perspectives on the interdisciplinary use of fuzzy logic theory, focusing on the application of sets and matrices. Highlighting theoretical framework and empirical research findings, this book is ideally designed for academics, practitioners, upper-level students, and professionals interested in an innovative overview of fuzzy logic sets and matrices.

Guide to Discrete Mathematics

An Accessible Introduction to the History, Theory, Logic and Applications

Author: Gerard O'Regan

Publisher: Springer

ISBN: 3319445618

Category: Computers

Page: 368

View: 6334

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.

Matrix Logic and Mind

A Probe into a Unified Theory of Mind and Matter

Author: A. Stern

Publisher: Elsevier

ISBN: 0080934137

Category: Mathematics

Page: 290

View: 757

In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies.

Computer Science – Theory and Applications

6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings

Author: Alexander Kulikov,Nikolay Vereshchagin

Publisher: Springer Science & Business Media

ISBN: 3642207111

Category: Computers

Page: 471

View: 3687

This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.

Code Design for Dependable Systems

Theory and Practical Applications

Author: Eiji Fujiwara

Publisher: John Wiley & Sons

ISBN: 047179273X

Category: Science

Page: 660

View: 2595

Theoretical and practical tools to master matrix code designstrategy and technique Error correcting and detecting codes are essential to improvingsystem reliability and have popularly been applied to computersystems and communication systems. Coding theory has been studiedmainly using the code generator polynomials; hence, the codes aresometimes called polynomial codes. On the other hand, the codesdesigned by parity check matrices are referred to in this book asmatrix codes. This timely book focuses on the design theory formatrix codes and their practical applications for the improvementof system reliability. As the author effectively demonstrates,matrix codes are far more flexible than polynomial codes, as theyare capable of expressing various types of code functions. In contrast to other coding theory publications, this one does notburden its readers with unnecessary polynomial algebra, but ratherfocuses on the essentials needed to understand and take fulladvantage of matrix code constructions and designs. Readers arepresented with a full array of theoretical and practical tools tomaster the fine points of matrix code design strategy andtechnique: * Code designs are presented in relation to practical applications,such as high-speed semiconductor memories, mass memories of disksand tapes, logic circuits and systems, data entry systems, anddistributed storage systems * New classes of matrix codes, such as error locating codes, spottybyte error control codes, and unequal error control codes, areintroduced along with their applications * A new parallel decoding algorithm of the burst error controlcodes is demonstrated In addition to the treatment of matrix codes, the author providesreaders with a general overview of the latest developments andadvances in the field of code design. Examples, figures, andexercises are fully provided in each chapter to illustrate conceptsand engage the reader in designing actual code and solving realproblems. The matrix codes presented with practical parametersettings will be very useful for practicing engineers andresearchers. References lead to additional material so readers canexplore advanced topics in depth. Engineers, researchers, and designers involved in dependable systemdesign and code design research will find the unique focus andperspective of this practical guide and reference helpful infinding solutions to many key industry problems. It also can serveas a coursebook for graduate and advanced undergraduate students.

Random Matrix Models and Their Applications

Author: Pavel Bleher,Alexander Its

Publisher: Cambridge University Press

ISBN: 9780521802093

Category: Mathematics

Page: 438

View: 4734

Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1490110127

Category: Mathematics

Page: 1037

View: 2993

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Boolean matrix theory and applications

Author: Ki Hang Kim

Publisher: N.A

ISBN: 9780824717889

Category: Mathematics

Page: 288

View: 9560

Decision Making in the Manufacturing Environment

Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods

Author: Ravipudi Venkata Rao

Publisher: Springer Science & Business Media

ISBN: 1846288193

Category: Business & Economics

Page: 374

View: 479

This book shows how graph theory and matrix approach, and fuzzy multiple attribute decision making methods can be used in manufacturing. It proposes a methodology that will make decision making in the manufacturing environment structured and systematic. The book uses case studies to present the applications of decision making methods in real manufacturing situations.

Computer Science - Theory and Applications

Fourth International Computer Science Symposium in Russia, CSR 2009, Novosibirsk, Russia, August 18-23, 2009, Proceedings

Author: Anna Frid,Andrei S. Morozov,Andrey Rybalchenko,Klaus W. Wagner

Publisher: Springer Science & Business Media

ISBN: 3642033504

Category: Computers

Page: 369

View: 4948

This book constitutes the refereed proceedings of the Fourth International Computer Science Symposium in Russia, CSR 2009, held in Novosibirsk, Russia, August 18-23, 2009. The 29 revised papers presented together with 4 invited papers were carefully reviewed and selected from 66 submissions. All major areas in computer science are addressed. The theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory and applications of logic to computer science.

Theoretical Advances and Applications of Fuzzy Logic and Soft Computing

Author: Oscar Castillo,Patricia Melin,Oscar Montiel Ross,Roberto Sepúlveda Cruz,Witold Pedrycz

Publisher: Springer Science & Business Media

ISBN: 3540724346

Category: Mathematics

Page: 626

View: 2033

This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1464966176

Category: Mathematics

Page: 459

View: 8855

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Probability, Combinatorics, and Chaos Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Probability, Combinatorics, and Chaos Theory in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Fuzzy Set Theory—and Its Applications

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9780792374350

Category: Business & Economics

Page: 514

View: 690

Since its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have been made in many directions. The primary goal of Fuzzy Set Theory - and its Applications, Fourth Edition is to provide a textbook for courses in fuzzy set theory, and a book that can be used as an introduction. To balance the character of a textbook with the dynamic nature of this research, many useful references have been added to develop a deeper understanding for the interested reader. Fuzzy Set Theory - and its Applications, Fourth Edition updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. Chapters have been updated and extended exercises are included.

Cost-Benefit Analysis and the Theory of Fuzzy Decisions

Identification and Measurement Theory

Author: K. K. Dompere

Publisher: Springer Science & Business Media

ISBN: 9783540221548

Category: Business & Economics

Page: 399

View: 2500

This monograph is devoted to the identification and measurement theory of costs and benefits in a fuzzy information environment. The process of cost-benefit analysis is presented, requiring the development of real cost-benefit databases and the construction of cost-benefit criterion. These steps are accomplished with various theoretical constructs that provide sets of self-contained algorithms for application. This book integrates cost-benefit analysis, theory of fuzzy decisions and social decisions into unified decision algorithms accessible to practitioners, researchers, and graduate students. It features the essentials of fuzzy mathematics and algorithms in a comprehensive way, exposing a multi-disciplinary approach for the development of cost-benefit decision making in the framework of fuzziness and soft computing.

Concise Computer Mathematics

Tutorials on Theory and Problems

Author: Ovidiu Bagdasar

Publisher: Springer Science & Business Media

ISBN: 3319017519

Category: Computers

Page: 109

View: 6952

Adapted from a modular undergraduate course on computational mathematics, Concise Computer Mathematics delivers an easily accessible, self-contained introduction to the basic notions of mathematics necessary for a computer science degree. The text reflects the need to quickly introduce students from a variety of educational backgrounds to a number of essential mathematical concepts. The material is divided into four units: discrete mathematics (sets, relations, functions), logic (Boolean types, truth tables, proofs), linear algebra (vectors, matrices and graphics), and special topics (graph theory, number theory, basic elements of calculus). The chapters contain a brief theoretical presentation of the topic, followed by a selection of problems (which are direct applications of the theory) and additional supplementary problems (which may require a bit more work). Each chapter ends with answers or worked solutions for all of the problems.

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