fuzzy logic and mathematics a historical perspective

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Fuzzy Logic And Mathematics

Author : Radim Belohlavek
ISBN : 9780190200022
Genre : Mathematics
File Size : 65. 54 MB
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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.

Fuzzy Logic

Author : Paul P. Wang
ISBN : 9783540712589
Genre : Mathematics
File Size : 80. 20 MB
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How far can you take fuzzy logic, the brilliant conceptual framework made famous by George Klir? With this book, you can find out. The authors of this updated edition have extended Klir’s work by taking fuzzy logic into even more areas of application. It serves a number of functions, from an introductory text on the concept of fuzzy logic to a treatment of cutting-edge research problems suitable for a fully paid-up member of the fuzzy logic community.

Concepts And Fuzzy Logic

Author : Radim Bělohlávek
ISBN : 9780262016476
Genre : Philosophy
File Size : 76. 90 MB
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In this work - both psychologists working on concepts and mathematicians working on fuzzy logic - reassess the usefulness of fuzzy logic for the psychology of concepts.

Fuzzy Logic In Its 50th Year

Author : Cengiz Kahraman
ISBN : 9783319310930
Genre : Computers
File Size : 39. 91 MB
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This book offers a multifaceted perspective on fuzzy set theory, discussing its developments over the last 50 years. It reports on all types of fuzzy sets, from ordinary to hesitant fuzzy sets, with each one explained by its own developers, authoritative scientists well known for their previous works. Highlighting recent theorems and proofs, the book also explores how fuzzy set theory has come to be extensively used in almost all branches of science, including the health sciences, decision science, earth science and the social sciences alike. It presents a wealth of real-world sample applications, from routing problem to robotics, and from agriculture to engineering. By offering a comprehensive, timely and detailed portrait of the field, the book represents an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on new fuzzy set extensions.

Fuzzy Logic With Engineering Applications

Author : Timothy J. Ross
ISBN : 9780470748510
Genre : Technology & Engineering
File Size : 63. 81 MB
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The first edition of Fuzzy Logic with Engineering Applications (1995) was the first classroom text for undergraduates in the field. Now updated for the second time, this new edition features the latest advances in the field including material on expansion of the MLFE method using genetic algorithms, cognitive mapping, fuzzy agent-based models and total uncertainty. Redundant or obsolete topics have been removed, resulting in a more concise yet inclusive text that will ensure the book retains its broad appeal at the forefront of the literature. Fuzzy Logic with Engineering Applications, 3rd Edition is oriented mainly towards methods and techniques. Every chapter has been revised, featuring new illustrations and examples throughout. Supporting MATLAB code is downloadable at www.wileyeurope.com/go/fuzzylogic. This will benefit student learning in all basic operations, the generation of membership functions, and the specialized applications in the latter chapters of the book, providing an invaluable tool for students as well as for self-study by practicing engineers.

Mathematics Of Fuzzy Sets

Author : Ulrich Höhle
ISBN : 9781461550792
Genre : Mathematics
File Size : 29. 89 MB
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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.

Growing Explanations

Author : M. Norton Wise
ISBN : 9780822390084
Genre : Science
File Size : 90. 34 MB
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For much of the twentieth century scientists sought to explain objects and processes by reducing them to their components—nuclei into protons and neutrons, proteins into amino acids, and so on—but over the past forty years there has been a marked turn toward explaining phenomena by building them up rather than breaking them down. This collection reflects on the history and significance of this turn toward “growing explanations” from the bottom up. The essays show how this strategy—based on a widespread appreciation for complexity even in apparently simple processes and on the capacity of computers to simulate such complexity—has played out in a broad array of sciences. They describe how scientists are reordering knowledge to emphasize growth, change, and contingency and, in so doing, are revealing even phenomena long considered elementary—like particles and genes—as emergent properties of dynamic processes. Written by leading historians and philosophers of science, these essays examine the range of subjects, people, and goals involved in changing the character of scientific analysis over the last several decades. They highlight the alternatives that fields as diverse as string theory, fuzzy logic, artificial life, and immunology bring to the forms of explanation that have traditionally defined scientific modernity. A number of the essays deal with the mathematical and physical sciences, addressing concerns with hybridity and the materials of the everyday world. Other essays focus on the life sciences, where questions such as “What is life?” and “What is an organism?” are undergoing radical re-evaluation. Together these essays mark the contours of an ongoing revolution in scientific explanation. Contributors. David Aubin, Amy Dahan Dalmedico, Richard Doyle, Claus Emmeche, Peter Galison, Stefan Helmreich, Ann Johnson, Evelyn Fox Keller, Ilana Löwy, Claude Rosental, Alfred Tauber

Readings In Fuzzy Sets For Intelligent Systems

Author : Didier J. Dubois
ISBN : 9781483214504
Genre : Computers
File Size : 27. 45 MB
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Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered. Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed. This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.

The Oxford Handbook Of Computational Economics And Finance

Author : Shu-Heng Chen
ISBN : 9780190877507
Genre : Business & Economics
File Size : 62. 49 MB
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The Oxford Handbook of Computational Economics and Finance provides a survey of both the foundations of and recent advances in the frontiers of analysis and action. It is both historically and interdisciplinarily rich and also tightly connected to the rise of digital society. It begins with the conventional view of computational economics, including recent algorithmic development in computing rational expectations, volatility, and general equilibrium. It then moves from traditional computing in economics and finance to recent developments in natural computing, including applications of nature-inspired intelligence, genetic programming, swarm intelligence, and fuzzy logic. Also examined are recent developments of network and agent-based computing in economics. How these approaches are applied is examined in chapters on such subjects as trading robots and automated markets. The last part deals with the epistemology of simulation in its trinity form with the integration of simulation, computation, and dynamics. Distinctive is the focus on natural computationalism and the examination of the implications of intelligent machines for the future of computational economics and finance. Not merely individual robots, but whole integrated systems are extending their "immigration" to the world of Homo sapiens, or symbiogenesis.

Fuzzy Logic

Author : G. Gerla
ISBN : 9789401596602
Genre : Mathematics
File Size : 61. 61 MB
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Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh [1975]a). The aim of this theory is to formalize the "approximate reasoning" we use in everyday life, the object of investigation being the human aptitude to manage vague properties (as, for example, "beautiful", "small", "plausible", "believable", etc. ) that by their own nature can be satisfied to a degree different from 0 (false) and I (true). It is worth noting that the traditional deductive framework in many-valued logic is different from the one adopted in this book for fuzzy logic: in the former logics one always uses a "crisp" deduction apparatus, producing crisp sets of formulas, the formulas that are considered logically valid. By contrast, fuzzy logical deductive machinery is devised to produce a fuzzy set of formulas (the theorems) from a fuzzy set of formulas (the hypotheses). Approximate reasoning has generated a very interesting literature in recent years. However, in spite of several basic results, in our opinion, we are still far from a satisfactory setting of this very hard and mysterious subject. The aim of this book is to furnish some theoretical devices and to sketch a general framework for fuzzy logic. This is also in accordance with the non Fregean attitude of the book.

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