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Author : Jorma K. Mattila
Publisher :
ISBN 13 : 9789535103936
Total Pages : pages
Book Rating : 4.1/5 (39 download)
Download or read book Standard Fuzzy Sets and Some Many-Valued Logics written by Jorma K. Mattila and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrew Schumann
Publisher : Infinite Study
ISBN 13 : 159973026X
Total Pages : 123 pages
Book Rating : 4.5/5 (997 download)
Download or read book Neutrality and Many-Valued Logics written by Andrew Schumann and published by Infinite Study. This book was released on 2007 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Godel?s, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.
Author : Didier Dubois
Publisher : Springer Science & Business Media
ISBN 13 : 9401716528
Total Pages : 421 pages
Book Rating : 4.4/5 (17 download)
Download or read book Fuzzy Sets, Logics and Reasoning about Knowledge written by Didier Dubois and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.
Author : Elmer Dadios
Publisher : BoD – Books on Demand
ISBN 13 : 9535103938
Total Pages : 298 pages
Book Rating : 4.5/5 (351 download)
Download or read book Fuzzy Logic written by Elmer Dadios and published by BoD – Books on Demand. This book was released on 2012-03-28 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems.
Author : G. Gerla
Publisher : Springer Science & Business Media
ISBN 13 : 9401596603
Total Pages : 276 pages
Book Rating : 4.4/5 (15 download)
Download or read book Fuzzy Logic written by G. Gerla and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 1461550793
Total Pages : 722 pages
Book Rating : 4.4/5 (615 download)
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.
Author : Dov M. Gabbay
Publisher : Elsevier
ISBN 13 : 008054939X
Total Pages : 691 pages
Book Rating : 4.0/5 (85 download)
Download or read book The Many Valued and Nonmonotonic Turn in Logic written by Dov M. Gabbay and published by Elsevier. This book was released on 2007-08-13 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.
Author : Merrie Bergmann
Publisher : Cambridge University Press
ISBN 13 : 1139468782
Total Pages : 7 pages
Book Rating : 4.1/5 (394 download)
Download or read book An Introduction to Many-Valued and Fuzzy Logic written by Merrie Bergmann and published by Cambridge University Press. This book was released on 2008-01-14 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.
Author : Mikael Collan
Publisher : Springer
ISBN 13 : 3319269860
Total Pages : 225 pages
Book Rating : 4.3/5 (192 download)
Download or read book Fuzzy Technology written by Mikael Collan and published by Springer. This book was released on 2015-11-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a timely and comprehensive yet concise view on the field of fuzzy logic and its real-world applications. The chapters, written by authoritative scholars in the field, report on promising new models for data analysis, decision making, and systems modeling, with a special emphasis on their applications in management science. The book is a token of appreciation from the fuzzy research community to Professor Christer Carlsson for his long time research and organizational commitment, which have among other things resulted in the foundation and success of the Institute for Advanced Management Systems Research (IAMSR) at Åbo Akademi University, in Åbo (Turku), Finland. The book serves as timely guide for the fuzzy logic and operations research communities alike.
Author : Pranab Kumar Sen
Publisher : Allied Publishers
ISBN 13 : 9788170232940
Total Pages : 310 pages
Book Rating : 4.2/5 (329 download)
Download or read book Foundations of Logic and Language written by Pranab Kumar Sen and published by Allied Publishers. This book was released on 1990 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Radim Bělohlávek
Publisher : Oxford University Press
ISBN 13 : 0190200014
Total Pages : 545 pages
Book Rating : 4.1/5 (92 download)
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.
Author : George Bojadziev
Publisher : World Scientific
ISBN 13 : 9814499943
Total Pages : 299 pages
Book Rating : 4.8/5 (144 download)
Download or read book Fuzzy Sets, Fuzzy Logic, Applications written by George Bojadziev and published by World Scientific. This book was released on 1996-01-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications.
Author : Salvatore Greco
Publisher : Springer
ISBN 13 : 364231709X
Total Pages : 674 pages
Book Rating : 4.6/5 (423 download)
Download or read book Advances in Computational Intelligence, Part I written by Salvatore Greco and published by Springer. This book was released on 2012-07-20 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: These four volumes (CCIS 297, 298, 299, 300) constitute the proceedings of the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, held in Catania, Italy, in July 2012. The 258 revised full papers presented together with six invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy machine learning and on-line modeling; computing with words and decision making; soft computing in computer vision; rough sets and complex data analysis: theory and applications; intelligent databases and information system; information fusion systems; philosophical and methodological aspects of soft computing; basic issues in rough sets; 40th anniversary of the measures of fuziness; SPS11 uncertainty in profiling systems and applications; handling uncertainty with copulas; formal methods to deal with uncertainty of many-valued events; linguistic summarization and description of data; fuzzy implications: theory and applications; sensing and data mining for teaching and learning; theory and applications of intuitionistic fuzzy sets; approximate aspects of data mining and database analytics; fuzzy numbers and their applications; information processing and management of uncertainty in knowledge-based systems; aggregation functions; imprecise probabilities; probabilistic graphical models with imprecision: theory and applications; belief function theory: basics and/or applications; fuzzy uncertainty in economics and business; new trends in De Finetti's approach; fuzzy measures and integrals; multicriteria decision making; uncertainty in privacy and security; uncertainty in the spirit of Pietro Benvenuti; coopetition; game theory; probabilistic approach.
Author : Michael Gr. Voskoglou
Publisher : Infinite Study
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4./5 ( download)
Download or read book Multi Valued Logics: A Review written by Michael Gr. Voskoglou and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work, starting from the fuzzy sets theory introduced by Zadeh in 1965, reviews its generalizations and other relevant theories developed during the last 50 years. Those theories gave genesis to multi-valued logics, which help to treat better the uncertain or vague situations that frequently appear in problems of every day life, science and technology. Therefore they need not be seen as competitive, but as complementary to the traditional bi-valued logic of Aristotle. The article offers the basic framework to those wanting to study further the multi-valued logics that have found recently many and important applications to almost all sectors of the human activity.
Author : Petr Hájek
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003707
Total Pages : 316 pages
Book Rating : 4.0/5 (37 download)
Download or read book Metamathematics of Fuzzy Logic written by Petr Hájek and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 316 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.
Author : Rosanna Keefe
Publisher : MIT Press
ISBN 13 : 0262112256
Total Pages : 363 pages
Book Rating : 4.2/5 (621 download)
Download or read book Vagueness written by Rosanna Keefe and published by MIT Press. This book was released on 1996 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms-such as "tall", "red", "bald", and "tadpole" -- have borderline cases (arguably, someone may be neither tall nor not tall); and they lack well-defined extensions (there is no sharp boundary between tall people and the rest). The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate. Another striking problem to which vagueness gives rise is the sorites paradox. If you remove one grain from a heap of sand, surely you must be left with a heap. Yet apply this principle repeatedly as you remove grains one by one, and you end up, absurdly, with a solitary grain that counts as a heap. This anthology collects papers in the field. After an introduction that surveys the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent current work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity.
Author : Diederik Aerts
Publisher : Springer Science & Business Media
ISBN 13 : 9401728348
Total Pages : 251 pages
Book Rating : 4.4/5 (17 download)
Download or read book Quantum Structures and the Nature of Reality written by Diederik Aerts and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Structures and the Nature of Reality is a collection of papers written for an interdisciplinary audience about the quantum structure research within the International Quantum Structures Association. The advent of quantum mechanics has changed our scientific worldview in a fundamental way. Many popular and semi-popular books have been published about the paradoxical aspects of quantum mechanics. Usually, however, these reflections find their origin in the standard views on quantum mechanics, most of all the wave-particle duality picture. Contrary to relativity theory, where the meaning of its revolutionary ideas was linked from the start with deep structural changes in the geometrical nature of our world, the deep structural changes about the nature of our reality that are indicated by quantum mechanics cannot be traced within the standard formulation. The study of the structure of quantum theory, its logical content, its axiomatic foundation, has been motivated primarily by the search for their structural changes. Due to the high mathematical sophistication of this quantum structure research, no books have been published which try to explain the recent results for an interdisciplinary audience. This book tries to fill this gap by collecting contributions from some of the main researchers in the field. They reveal the steps that have been taken towards a deeper structural understanding of quantum theory.
