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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.
List of contents
1. Introduction. -2. Basic Concepts. -3. Fuzzy Calculus. -4. Fuzzy Differential Equations. -Mathematical Background. -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.
Additional text
“The book under review is aimed at presenting several interpretations of fuzzy initial value problems (FIVPs) for FDEs. … Each chapter is supplied with examples that allow for intuition in the theory of FDEs. Also, each chapter ends with its own list of references. This publication is a fine introductory textbook for everyone who is interested in the theory of deterministic differential equations operating in a fuzzy environment.” (Marek T. Malinowski, Mathematical Reviews, May, 2016)
“The book ‘Fuzzy differential equations in various approaches’ focuses on fuzzy differential equations (FDEs) and explains the basics of various approaches of FDEs. … Sufficient references are given at the end of each chapter and a small index is provided in the book. This precisely written book is concise and includes many examples to illustrate different approaches of FDEs. This book is worthy and can be recommended for graduate students or for researchers who work with uncertain dynamical systems.” (Krishnan Balachandran, zbMATH 1338.34005, 2016)
Report
"The book under review is aimed at presenting several interpretations of fuzzy initial value problems (FIVPs) for FDEs. ... Each chapter is supplied with examples that allow for intuition in the theory of FDEs. Also, each chapter ends with its own list of references. This publication is a fine introductory textbook for everyone who is interested in the theory of deterministic differential equations operating in a fuzzy environment." (Marek T. Malinowski, Mathematical Reviews, May, 2016)
"The book 'Fuzzy differential equations in various approaches' focuses on fuzzy differential equations (FDEs) and explains the basics of various approaches of FDEs. ... Sufficient references are given at the end of each chapter and a small index is provided in the book. This precisely written book is concise and includes many examples to illustrate different approaches of FDEs. This book is worthy and can be recommended for graduate students or for researchers who work with uncertain dynamical systems." (Krishnan Balachandran, zbMATH 1338.34005, 2016)
