Fuzzy Logic Of Quasi Truth An Algebraic Treatment

Author : Antonio Di Nola,Revaz Grigolia,Esko Turunen
Publisher : Springer
Page : 116 pages
File Size : 44,8 Mb
Release : 2016-03-18
Category : Technology & Engineering
ISBN : 9783319304069

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Fuzzy Logic of Quasi-Truth: An Algebraic Treatment by Antonio Di Nola,Revaz Grigolia,Esko Turunen Pdf

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values. However, it is complete with respect to all linearly ordered MV –algebras. As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.

Author : Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 545 pages
File Size : 40,9 Mb
Release : 2017
Category : Mathematics
ISBN : 9780190200015

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Fuzzy Logic and Mathematics by Radim Bělohlávek,Joseph W. Dauben,George J. Klir Pdf

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 : John Harding,Carol L. Walker,Elbert Walker
Publisher : Chapman & Hall/CRC
Page : 0 pages
File Size : 49,7 Mb
Release : 2016
Category : Algebra
ISBN : 1498735274

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The Truth Value Algebra of Type-2 Fuzzy Sets by John Harding,Carol L. Walker,Elbert Walker Pdf

Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explores the fundamental properties of this algebra and the role of these properties in applications. Accessible to anyone with a standard undergraduate mathematics background, this self-contained book offers several options for a one- or two-semester course. It covers topics increasingly used in fuzzy set theory, such as lattice theory, analysis, category theory, and universal algebra. The book discusses the basics of the type-2 truth value algebra, its subalgebra of convex normal functions, and their applications. It also examines the truth value algebra from a more algebraic and axiomatic view.

Author : Petr Cintula,Christian G Fermueller,Carles Noguera
Publisher : Unknown
Page : 384 pages
File Size : 51,8 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 1848901933

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Handbook of Mathematical Fuzzy Logic by Petr Cintula,Christian G Fermueller,Carles Noguera Pdf

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Renyi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness."

Author : Franco Montagna
Publisher : Springer
Page : 0 pages
File Size : 48,8 Mb
Release : 2016-09-10
Category : Mathematics
ISBN : 3319382950

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

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 : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 47,6 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9783319062334

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

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 : Yang Xu,Da Ruan,Keyun Qin,Jun Liu
Publisher : Springer
Page : 397 pages
File Size : 48,9 Mb
Release : 2012-11-02
Category : Technology & Engineering
ISBN : 9783540448471

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Lattice-Valued Logic by Yang Xu,Da Ruan,Keyun Qin,Jun Liu Pdf

Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.

Author : Dennis H. Rouvray
Publisher : Academic Press
Page : 387 pages
File Size : 46,7 Mb
Release : 1997-04-18
Category : Science
ISBN : 9780080532257

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Fuzzy Logic in Chemistry by Dennis H. Rouvray Pdf

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

Author : Ángel Garrido,Urszula Wybraniec-Skardowska
Publisher : Birkhäuser
Page : 815 pages
File Size : 55,9 Mb
Release : 2018-06-12
Category : Mathematics
ISBN : 9783319654300

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The Lvov-Warsaw School. Past and Present by Ángel Garrido,Urszula Wybraniec-Skardowska Pdf

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

Author : Nikolaos Galatos,Kazushige Terui
Publisher : Springer Nature
Page : 382 pages
File Size : 48,9 Mb
Release : 2021-12-13
Category : Philosophy
ISBN : 9783030769208

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Hiroakira Ono on Substructural Logics by Nikolaos Galatos,Kazushige Terui Pdf

This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.

Author : Anonim
Publisher : Unknown
Page : 1078 pages
File Size : 45,6 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015055144714

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Mathematical Reviews by Anonim Pdf

Author : Ronei Marcos de Moraes,Etienne E Kerre,Liliane dos Santos Machado,Jie Lu
Publisher : World Scientific
Page : 780 pages
File Size : 45,5 Mb
Release : 2014-07-07
Category : Computers
ISBN : 9789814623001

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Decision Making and Soft Computing by Ronei Marcos de Moraes,Etienne E Kerre,Liliane dos Santos Machado,Jie Lu Pdf

FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the 11th of FLINS conference cover state-of-the-art research, development, and technology for computational intelligence systems, both from the foundations and the applications points-of-view. Contents:Invited Lectures:The Contribution of Fuzzy Sets to Decision Sciences (D Dubois)Granular Fuzzy Systems: A New Direction in Soft Computing and Human Centric Decision-Making (Witold Pedrycz)Some Approaches Towards Lattice Computing in Mathematical Morphology and Computational Intelligence (Peter Sussner)Decision Making and Decision Support SystemsStatistics, Data Analysis and Data MiningFoundations of Computational IntelligenceSoft Computing and Applied ResearchIntelligent Systems and Knowledge EngineeringUncertainty ModelingIntelligent Information Processing Readership: Graduate students, researchers, and academics in artificial intelligence/machine learning, information management, decision sciences, databases/information sciences and fuzzy logic. Keywords:FLINS 2014;Soft Computing;Knowledge Engineering;Decision Making

Author : Xianyi Zeng,Jie Lu,Etienne E Kerre,Luis Martinez,Ludovic Koehl
Publisher : World Scientific
Page : 1208 pages
File Size : 43,5 Mb
Release : 2016-07-14
Category : Computers
ISBN : 9789813146983

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Uncertainty Modelling in Knowledge Engineering and Decision Making by Xianyi Zeng,Jie Lu,Etienne E Kerre,Luis Martinez,Ludovic Koehl Pdf

FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to include Computational Intelligence for applied research. The contributions to the 12th of FLINS conference cover state-of-the-art research, development, and technology for computational intelligence systems, both from the foundations and the applications points-of-view.

Author : Cengiz Kahraman,Faik Tunc Bozbura,Etienne E Kerre
Publisher : World Scientific
Page : 1372 pages
File Size : 44,6 Mb
Release : 2012-08-10
Category : Computers
ISBN : 9789814417754

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Uncertainty Modeling In Knowledge Engineering And Decision Making - Proceedings Of The 10th International Flins Conference by Cengiz Kahraman,Faik Tunc Bozbura,Etienne E Kerre Pdf

FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the 10th of FLINS conference cover state-of-the-art research, development, and technology for computational intelligence systems, both from the foundations and the applications points-of-view.

Author : Anonim
Publisher : Unknown
Page : 590 pages
File Size : 44,6 Mb
Release : 1997
Category : Classification
ISBN : NWU:35556030862106

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International Classification by Anonim Pdf