Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales

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.

Generalized Hukuhara Difference and Division for Interval and Fuzzy Arithmetic.- An Embedding Theorem and the Multiplication of Fuzzy Vectors.- Calculus of Fuzzy Vector-valued Functions on Time Scales.- Shift Almost Periodic Fuzzy Vector-valued Functions.- Division of Fuzzy Vector-valued Functions Depending on a Determinant Algorithm.- Almost Periodic Generalized Fuzzy Multidimensional Dynamic Equations and Applications.