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Author Gomes, Luciana Takata,
Title Fuzzy differential equations in various approaches / Luciana Takata Gomes, Laecio Carvalho de Barros, Barnabas Bede.
Imprint Cham : Springer, 2015.

View online
View online
Author Gomes, Luciana Takata,
Series SpringerBriefs in mathematics, 2191-8201
SpringerBriefs in mathematics. 2191-8201
Subject Differential equations.
Fuzzy mathematics.
Alt Name Barros, Laécio Carvalho de,
Bede, Barnabas,
Description 1 online resource : illustrations.
polychrome rdacc
Bibliography Note Includes bibliographical references and index.
Summary This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems. Beginning with a historical overview and introduction to fundamental notions of fuzzy sets, including different possibilities of fuzzy differentiation and metric spaces, this book moves on to an overview of fuzzy calculus thorough exposition and comparison of different approaches. Innovative theories of fuzzy calculus and fuzzy differential equations using fuzzy bunches of functions are introduced and explored. Launching with a brief review of essential theories, this book investigates both well-known and novel approaches in this field; such as the Hukuhara differentiability and its generalizations as well as differential inclusions and Zadeh's extension. Through a unique analysis, results of all these theories are examined and compared.
Contents Machine generated contents note: 1. Introduction -- 1.1. Initial Value Problems -- 1.2. Fuzzy Initial Value Problem -- 1.2.1. Historical Overview -- References -- 2. Basic Concepts -- 2.1. Fuzzy Subsets -- 2.2. Extension Principle -- 2.3. Fuzzy Arithmetics for Fuzzy Numbers -- 2.3.1. Standard Interval Arithmetic and Extension Principle -- 2.3.2. Interactive Arithmetic -- 2.3.3. Constraint Interval Arithmetic -- 2.3.4. Hukuhara and Generalized Differences -- 2.4. Fuzzy Metric Spaces -- 2.5. Fuzzy Functions -- 2.6. Summary -- References -- 3. Fuzzy Calculus -- 3.1. Fuzzy Calculus for Fuzzy-Set-Valued Functions -- 3.1.1. Integrals -- 3.1.2. Derivatives -- 3.1.3. Fundamental Theorem of Calculus -- 3.2. Fuzzy Calculus for Fuzzy Bunches of Functions -- 3.2.1. Integral -- 3.2.2. Derivative -- 3.2.3. Fundamental Theorem of Calculus -- 3.3. Comparison -- 3.4. Summary -- References -- 4. Fuzzy Differential Equations -- 4.1. Approaches of FIVPs -- 4.1.1. Fuzzy Differential Equations with Fuzzy Derivatives -- 4.1.2. Fuzzy Differential Inclusions -- 4.1.3. Extension of the Solution -- 4.2. Hukuhara Derivative -- 4.3. Strongly Generalized Derivative -- 4.4. Fuzzy Differential Inclusions -- 4.5. Extension of the Solution -- 4.5.1. Autonomous FIVP with Fuzzy Initial Condition -- 4.5.2. FIVP with Fuzzy Initial Condition and Fuzzy Parameter -- 4.6. Extension of the Derivative Operator -- 4.7. Summary -- References -- Mathematical Background -- A.1. Continuity and Semicontinuity -- A.2. Spaces of Functions.
Note Online resource; title from PDF title page (EBSCO, viewed September 11, 2015).
ISBN 9783319225753 (electronic bk.)
3319225758 (electronic bk.)
331922574X (print)
9783319225746 (print)
ISBN/ISSN 10.1007/978-3-319-22575-3
OCLC # 920519631
Additional Format Printed edition: 9783319225746

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