Fuzzy Differential Equations in various Approaches

Description

Preface......Page 3 Contents......Page 5 Symbols......Page 7 1 Introduction......Page 9 Fuzzy Initial Value Problem......Page 11 Refs......Page 16 Fuzzy Subsets......Page 19 Extension Principle......Page 24 Fuzzy Arithmetics for Fuzzy Numbers......Page 27 Standard Interval Arithmetic & Extension Principle......Page 28 Interactive Arithmetic......Page 29 Constraint Interval Arithmetic......Page 30 Hukuhara & Generalized Differences......Page 31 Fuzzy Metric Spaces......Page 33 Fuzzy Functions......Page 36 Summary......Page 46 Refs......Page 47 Integrals......Page 49 Derivatives......Page 51 Fundamental Theorem of Calculus......Page 57 Integral......Page 58 Derivative......Page 61 Fundamental Theorem of Calculus......Page 65 Comparison......Page 66 Refs......Page 74 Approaches of FIVPs......Page 76 Fuzzy DEs with Fuzzy Derivatives......Page 77 Fuzzy Differential Inclusions......Page 78 Extension of the Solution......Page 79 Hukuhara Derivative......Page 81 Strongly Generalized Derivative......Page 90 Fuzzy Differential Inclusions......Page 98 Extension of the Solution......Page 103 Autonomous FIVP with Fuzzy Initial Condition......Page 105 FIVP with Fuzzy Initial Condition & Fuzzy Parameter......Page 106 Extension of the Derivative Operator......Page 108 Summary......Page 118 Refs......Page 119 Mathematical Background......Page 121 Index......Page 124