This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.
Author(s): Chao Wang, Ravi P. Agarwal
Series: Synthesis Lectures on Mathematics & Statistics
Publisher: Springer
Year: 2022
Language: English
Pages: 194
City: Cham
Preface
Contents
1 Generalized Hukuhara Difference and Division for Interval and Fuzzy Arithmetic
1.1 Generalized Hukuhara Difference and Properties
1.2 The Case of Compact Intervals in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript n) /StPNE pdfmark [/StBMC pdfmarkmathbbRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark
1.3 ps: [/EMC pdfmark [/Subtype /Span /ActualText (g upper H) /StPNE pdfmark [/StBMC pdfmarkgHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Difference of Fuzzy Numbers
1.3.1 Support Functions and Fuzzy ps: [/EMC pdfmark [/Subtype /Span /ActualText (g upper H) /StPNE pdfmark [/StBMC pdfmarkgHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Difference
1.3.2 A Decomposition of Fuzzy Numbers and ps: [/EMC pdfmark [/Subtype /Span /ActualText (g upper H) /StPNE pdfmark [/StBMC pdfmarkgHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Difference
1.3.3 Approximated Fuzzy ps: [/EMC pdfmark [/Subtype /Span /ActualText (g upper H) /StPNE pdfmark [/StBMC pdfmarkgHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Difference
1.4 Generalized Division
1.4.1 The Fuzzy Case
1.4.2 Approximated Fuzzy ps: [/EMC pdfmark [/Subtype /Span /ActualText (MathID1215) /StPNE pdfmark [/StBMC pdfmarkgps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Division
1.5 Applications of ps: [/EMC pdfmark [/Subtype /Span /ActualText (MathID1237) /StPNE pdfmark [/StBMC pdfmarkgHps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Difference and ps: [/EMC pdfmark [/Subtype /Span /ActualText (MathID1238) /StPNE pdfmark [/StBMC pdfmarkgps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark-Division
1.5.1 Interval and Fuzzy Algebraic Equations
1.5.2 Interval and Fuzzy Differential Equations
2 An Embedding Theorem and Multiplication of Fuzzy Vectors
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2.1 An Embedding Theorem for Fuzzy Multidimensional Space
2.2 Multiplication of Fuzzy Vectors in Fuzzy Multidimensional Space
3 Calculus of Fuzzy Vector-Valued Functions on Time Scales
3.1 g upper HgH-upper Delta-Derivative of Fuzzy Vector-Valued Functions on Time Scales
3.2 upper Delta-Integral of Fuzzy Vector-Valued Functions on Time Scales
4 Shift Almost Periodic Fuzzy Vector-Valued Functions
4.1 Shift Operators on Time Scales
4.1.1 Shift Operators
4.1.2 Periodicity of Time Scales
4.2 Complete-Closed Time Scales Under Non-translational Shifts
4.3 Shift Almost Periodic Fuzzy Vector-Valued Functions
5 Division of Fuzzy Vector-Valued Functions Depending on Determinant Algorithm
5.1 Basic Results of Fuzzy Multidimensional Spaces
5.2 A New Division of Multidimensional Intervals and Fuzzy Vectors
5.3 Basic Results of Calculus of Fuzzy Vector-Valued Functions on Time Scales
6 Almost Periodic Generalized Fuzzy Multidimensional Dynamic Equations and Applications
6.1 Almost Periodic Generalized Fuzzy Multidimensional Dynamic Equations
6.2 Applications on Fuzzy Dynamic Equations and Models on Time Scales
A Almost Anti-periodic Discrete Oscillation
A.1 Almost Anti-periodic Discrete Functions
A.2 Almost Anti-periodic Oscillation of the Mechanical System
A.2.1 Existence and Uniqueness of the Almost Anti-periodic Solution
A.2.2 Stability of the Almost Anti-periodic Solutions
A.3 Almost Anti-periodic Functions on Time Scales
Appendix References
Index
