Download or read book A Modern Introduction to Fuzzy Mathematics written by Apostolos Syropoulos and published by John Wiley & Sons. This book was released on 2020-07-28 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides readers with the foundations of fuzzy mathematics as well as more advanced topics A Modern Introduction to Fuzzy Mathematics provides a concise presentation of fuzzy mathematics., moving from proofs of important results to more advanced topics, like fuzzy algebras, fuzzy graph theory, and fuzzy topologies. The authors take the reader through the development of the field of fuzzy mathematics, starting with the publication in 1965 of Lotfi Asker Zadeh's seminal paper, Fuzzy Sets. The book begins with the basics of fuzzy mathematics before moving on to more complex topics, including: Fuzzy sets Fuzzy numbers Fuzzy relations Possibility theory Fuzzy abstract algebra And more Perfect for advanced undergraduate students, graduate students, and researchers with an interest in the field of fuzzy mathematics, A Modern Introduction to Fuzzy Mathematics walks through both foundational concepts and cutting-edge, new mathematics in the field.

Download or read book Fuzzy Mathematics written by John N. Mordeson and published by Physica. This book was released on 2012-11-08 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor "and", sup for "or") to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper "Fuzzy groups", which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.

Download or read book Mathematics of Fuzzy Sets and Fuzzy Logic written by Barnabas Bede and published by Springer. This book was released on 2012-12-14 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.

Download or read book Fuzzy Logic and Mathematics written by Radim Bělohlávek and published by Oxford University Press. This book was released on 2017 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fuzzy Mathematics in Economics and Engineering written by James J. Buckley and published by Physica. This book was released on 2013-06-05 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims at surveying results in the application of fuzzy sets and fuzzy logic to economics and engineering. New results include fuzzy non-linear regression, fully fuzzified linear programming, fuzzy multi-period control, fuzzy network analysis, each using an evolutionary algorithm; fuzzy queuing decision analysis using possibility theory; fuzzy differential equations; fuzzy difference equations; fuzzy partial differential equations; fuzzy eigenvalues based on an evolutionary algorithm; fuzzy hierarchical analysis using an evolutionary algorithm; fuzzy integral equations. Other important topics covered are fuzzy input-output analysis; fuzzy mathematics of finance; fuzzy PERT (project evaluation and review technique). No previous knowledge of fuzzy sets is needed. The mathematical background is assumed to be elementary calculus.

Download or read book Fuzzy Mathematics written by Etienne E. Kerre and published by MDPI. This book was released on 2018-11-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics

Download or read book Mathematics of Fuzzy Sets written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Download or read book Mathematics of Fuzziness Basic Issues written by Xuzhu Wang and published by Springer. This book was released on 2009-03-11 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Fuzziness – Basic Issues introduces a basic notion of ‘fuzziness’ and provides a conceptual mathematical framework to characterize such fuzzy phenomena in Studies in Fuzziness and Soft Computing. The book systematically presents a self-contained introduction to the essentials of mathematics of fuzziness ranging from fuzzy sets, fuzzy relations, fuzzy numbers, fuzzy algebra, fuzzy measures, fuzzy integrals, and fuzzy topology to fuzzy control in a strictly mathematical manner. It contains most of the authors’ research results in the field of fuzzy set theory and has evolved from the authors’ lecture notes to both undergraduate and graduate students over the last three decades. A lot of exercises in each chapter of the book are particularly suitable as a textbook for any undergraduate and graduate student in mathematics, computer science and engineering. The reading of the book will surely lay a solid foundation for further research on fuzzy set theory and its applications.

Download or read book Mathematics Behind Fuzzy Logic written by Esko Turunen and published by Physica. This book was released on 1999-09-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Principles of Fuzzy Logic written by Vilém Novák and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A First Course in Fuzzy Logic written by Hung T. Nguyen and published by CRC Press. This book was released on 2005-10-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world a

Download or read book Recent Advances in Intuitionistic Fuzzy Logic Systems and Mathematics written by Said Melliani and published by Springer Nature. This book was released on 2020-10-12 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. Covering topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations, it discusses applications such as fuzzy real-time scheduling, intelligent control, diagnostics and time series prediction. The book features selected contributions presented at the 6th international congress of the Moroccan Applied Mathematics Society, which took place at Sultan Moulay Slimane University Beni Mellal, Morocco, from 7 to 9 November 2019.

Download or read book Fuzzy Mathematics Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2010-01-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of Fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of Fuzzy Positive linear operators to Fuzzy unit operator, the so-called Fuzzy Korovkin Theory. The related Fuzzy Global Smoothness is included. Then follows the study of Fuzzy Wavelet type operators and their convergence with rates to Fuzzy unit operator. Similarly the Fuzzy Neural Network Operators are discussed followed by Fuzzy Random Korovkin approximation theory and Fuzzy Random Neural Network approximations. The author continues with Fuzzy Korovkin approximations in the sense of Summability. Finally fuzzy sense differences of Fuzzy Wavelet type operators are estimated. The monograph's approach is quantitative and the main results are given via Fuzzy inequalities, involving Fuzzy moduli of continuity, that is Fuzzy Jackson type inequalities. The exposed theory is destined and expected to find applications to all aspects of Fuzziness from theoretical to practical in almost all sciences, technology, finance and industry. Also it has its interest within Pure Mathematics. So this monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering.

Download or read book Data Engineering written by Olaf Wolkenhauer and published by John Wiley & Sons. This book was released on 2004-04-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Metamathematics of Fuzzy Logic written by Petr Hájek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Download or read book Fuzzy Mathematical Programming written by Young-Jou Lai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory,artificial intelligence/expert system, etc. In this volume, methods and applications of fuzzy mathematical programming and possibilistic mathematical programming are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, we present solutions for real-world problems including production/manufacturing, transportation, assignment, game, environmental management, resource allocation, project investment, banking/finance, and agricultural economics. To improve flexibility and robustness of fuzzy mathematical programming techniques, we also present our expert decision-making support system IFLP which considers and solves all possibilities of a specific domain of (fuzzy) linear programming problems. Basic fuzzy set theories, membership functions, fuzzy decisions, operators and fuzzy arithmetic are introduced with simple numerical examples in aneasy-to-read and easy-to-follow manner. An updated bibliographical listing of 60 books, monographs or conference proceedings, and about 300 selected papers, reports or theses is presented in the end of this study.

Download or read book An Introduction to Fuzzy Logic and Fuzzy Sets written by James J. Buckley and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.