Fuzzy Equational Logic
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Fuzzy Equational Logic
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Author : Radim Belohlávek
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-26
Fuzzy Equational Logic written by Radim Belohlávek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-26 with Computers categories.
Fuzzy Mathematics In Economics And Engineering
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Author : James J. Buckley
language : en
Publisher: Physica
Release Date : 2013-06-05
Fuzzy Mathematics In Economics And Engineering written by James J. Buckley and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Business & Economics categories.
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.
An Introduction To Fuzzy Logic And Fuzzy Sets
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Author : James J. Buckley
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-11
An Introduction To Fuzzy Logic And Fuzzy Sets written by James J. Buckley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-11 with Computers categories.
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.
Mathematics Of Fuzzy Sets And Fuzzy Logic
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Author : Barnabas Bede
language : en
Publisher: Springer
Release Date : 2012-12-14
Mathematics Of Fuzzy Sets And Fuzzy Logic written by Barnabas Bede and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
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.
Fuzzy Logic And Mathematics
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Author : Radim Bělohlávek
language : en
Publisher: Oxford University Press
Release Date : 2017
Fuzzy Logic And Mathematics written by Radim Bělohlávek and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
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.
The Many Valued And Nonmonotonic Turn In Logic
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2007-08-13
The Many Valued And Nonmonotonic Turn In Logic written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
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.
Mathematics Behind Fuzzy Logic
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Author : Esko Turunen
language : en
Publisher: Physica
Release Date : 1999-09-24
Mathematics Behind Fuzzy Logic written by Esko Turunen and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-24 with Business & Economics categories.
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.
Fuzzy Fractional Differential Operators And Equations
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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2020-06-15
Fuzzy Fractional Differential Operators And Equations written by Tofigh Allahviranloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-15 with Technology & Engineering categories.
This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.
Mathematics Of Fuzzy Sets
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Author : Ulrich Höhle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Of Fuzzy Sets written by Ulrich Höhle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Knowledge Representation Techniques
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Author : Patrick Doherty
language : en
Publisher: Springer
Release Date : 2007-05-31
Knowledge Representation Techniques written by Patrick Doherty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-31 with Computers categories.
1. 1 Background The basis for the material in this book centers around research done in an ongoing long-term project which focuses on the development of highly au- 1 tonomousunmannedaerialvehiclesystems. Theactualplatformwhichserves as a case study for the research in this book will be described in detail later in this chapter. Before doing that, a brief background of the motivations - hind this research will be provided. One of the main research topics in the project is knowledge representation and reasoning and its use in Uav pl- forms. A very strong constraint has been placed on the nature of research done in the project where theoretical results, to the greatest extent possible, should serve as a basis for tractable reasoning mechanisms for use in a fully deployed autonomous Uav operating under soft real-time constraints asso- ated with the types of mission scenarios envisioned. Considering that much of the work with knowledge representation in this context focuses on application domains where one can only hope for an incomplete characterization of such domains, this methodological constraint has proven to be quite challenging since, in essence, the focus is on tractable approximate and nonmonotonic reasoning systems. As is well known, until recently, nonmonotonic formalisms have had a notorious reputation for lack of tractable and scalable reasoning systems.