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Author: Radim Bělohlávek
Publisher: Oxford University Press
ISBN: 0190200014
Category : Mathematics
Languages : en
Pages : 545
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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.
Author: Radim Bělohlávek
Publisher: Oxford University Press
ISBN: 0190200014
Category : Mathematics
Languages : en
Pages : 545
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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.
Author: Vilém Novák
Publisher: Springer Science & Business Media
ISBN: 1461552176
Category : Mathematics
Languages : en
Pages : 327
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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.
Author: Daniel Mcneill
Publisher: Simon and Schuster
ISBN: 0671875353
Category : Business & Economics
Languages : en
Pages : 324
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Book Description
Traces the story of Lofti Zadeh, an Iranian-American professor at Berkeley who began developing fuzzy logic - the way to program computers so they can mimic the imprecise way that humans make decisions.
Author: Radim Belohlavek
Publisher: Oxford University Press
ISBN: 019066570X
Category : Philosophy
Languages : en
Pages : 545
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Book Description
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.
Author: Franco Montagna
Publisher: Springer
ISBN: 3319062336
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.
Author: Susan Haack
Publisher: University of Chicago Press
ISBN: 9780226311333
Category : Philosophy
Languages : en
Pages : 324
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Book Description
Initially proposed as rivals of classical logic, alternative logics have become increasingly important in areas such as computer science and artificial intelligence. Fuzzy logic, in particular, has motivated major technological developments in recent years. Susan Haack's Deviant Logic provided the first extended examination of the philosophical consequences of alternative logics. In this new volume, Haack includes the complete text of Deviant Logic, as well as five additional papers that expand and update it. Two of these essays critique fuzzy logic, while three augment Deviant Logic's treatment of deduction and logical truth. Haack also provides an extensive new foreword, brief introductions to the new essays, and an updated bibliography of recent work in these areas. Deviant Logic, Fuzzy Logic will be indispensable to students of philosophy, philosophy of science, linguistics, mathematics, and computer science, and will also prove invaluable to experienced scholars working in these fields.
Author: Hanns-Werner Heister
Publisher: Springer Nature
ISBN: 3662629070
Category : Technology & Engineering
Languages : en
Pages : 724
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Book Description
This book unfolds the manifold, complex and intertwined relations between Fuzzy Logic and music in a first comprehensive overview on this topic: systematically as an outline, as completely as possible, in the aspects of Fuzzy Logic in this relation, and especially in music as a process with three main phases, five anthropological layers, and thirteen forms of existence of the art work (Classics, Jazz, Pop, Folklore). Being concerned with the ontological, gnoseological, psychological, and (music-) aesthetical status and the relative importance of different phenomena of relationship between music and Fuzzy Logic, the explication follows the four main principles (with five phenotypes) of Fuzzy Logic with respect to music: similarity, sharpening 1 as filtering, sharpening 2 as crystallization, blurring, and variation. The book reports on years of author’s research on topics that have been only little explored so far in the area of Music and Fuzzy Logic. It merges concepts of music analysis with fuzzy logical modes of thinking, in a unique way that is expected to attract both specialists of music and specialists of Fuzzy Logic, and also non-specialists in both fields. The book introduces the concept of dialectic between sharpening and – conscious – “blurring”. In turn, some important aspects of this dialectic are discussed, placing them in an historical dimension, and ending in the postulation of a 'musical turn' in the sciences, with some important reflections concerning a “Philosophy of Fuzzy Logic”. Moreover, a production-oriented thinking is borrowed from fuzzy logic to musicology in this book, opening new perspectives in music, and possibly also in other artistic fields.
Author: Dov M. Gabbay
Publisher: Clarendon Press
ISBN: 019159010X
Category : Mathematics
Languages : en
Pages : 494
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Book Description
Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.
Author: Harry J Gensler
Publisher: Routledge
ISBN: 1136994521
Category : Philosophy
Languages : en
Pages : 510
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Book Description
Introduction to Logic combines likely the broadest scope of any logic textbook available with clear, concise writing and interesting examples and arguments. Its key features, all retained in the Second Edition, include: • simpler ways to test arguments than those available in competing textbooks, including the star test for syllogisms • a wide scope of materials, making it suitable for introductory logic courses (as the primary text) or intermediate classes (as the primary or supplementary book) • engaging and easy-to-understand examples and arguments, drawn from everyday life as well as from the great philosophers • a suitability for self-study and for preparation for standardized tests, like the LSAT • a reasonable price (a third of the cost of many competitors) • exercises that correspond to the LogiCola program, which may be downloaded for free from the web. This Second Edition also: • arranges chapters in a more useful way for students, starting with the easiest material and then gradually increasing in difficulty • provides an even broader scope with new chapters on the history of logic, deviant logic, and the philosophy of logic • expands the section on informal fallacies • includes a more exhaustive index and a new appendix on suggested further readings • updates the LogiCola instructional program, which is now more visually attractive as well as easier to download, install, update, and use.
Author: Dennis H. Rouvray
Publisher: Academic Press
ISBN: 008053225X
Category : Science
Languages : en
Pages : 387
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Book Description
Fuzzy Logic has gained increasing acceptance as a way to deal with complexity and uncertainty in many areas of science and engineering. This book is the first to address its practical applications to chemical systems. Ten distinguished authors discuss the role of fuzzy logic in the characterization of a variety of chemical concepts, including chirality, quantum systems, molecular engineering and design, and hierarchical classification methods. Fuzzy Logic in Chemistry will appeal to both students and professionals who are seeking to learn more about theory and applications in an area of growing importance to the physical sciences. - The first book on the applications of fuzzy logic in chemistry - Covers a topic relevant to many disciplines, including molecular design - Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area - Features chapters from highly distinguished authors in the physical sciences
