Название: Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales
Автор: Chao Wang, Ravi P. Agarwal
Издательство: Springer
Год: 2022
Страниц: 195
Язык: английский
Формат: pdf (true), epub
Размер: 20.3 MB

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.

In addition, this book:

Introduces readers to the almost periodic theory of fuzzy dynamical equations on time scales
Presents comprehensive real-world applications in industrial engineering, systems science, and cybernetics
Includes cutting-edge research results and a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems)

We organize this book into six chapters.
In Chap. 1, some necessary knowledge of interval and fuzzy arithmetic is presented. A generalization of the Hukuhara difference is introduced. First, the case of compact convex sets is investigated which are applied to generalize the Hukuhara difference of fuzzy numbers by using their compact and convex level-cuts. Moreover, a similar approach is presented to propose a generalization of division for real intervals and fuzzy numbers. Some applications are provided to solve interval and fuzzy linear equations and fuzzy differential equations.
In Chap. 2, an embedding theorem for fuzzy multidimensional space is established and two new types of multiplication of fuzzy vectors are introduced and studied.
In Chap. 3, we introduce the basic notions of gH-derivatives of fuzzy vector-valued functions on time scales and obtain their fundamental properties. Moreover, the integral of fuzzy vector-valued functions is introduced and studied. Some basic results related to calculus of fuzzy vector-valued functions are established on time scales.
In Chap. 4, some necessary knowledge of shift operators and a generalized periodic time scales is presented. A notion of shift almost periodic fuzzy vector-valued functions is addressed and studied on complete-closed time scales under non-translational shifts, some fundamental results of shift almost periodic fuzzy vector-valued functions are established.
In Chap. 5, some basic results of fuzzy multidimensional spaces are demonstrated and a new division of multidimensional intervals and fuzzy vectors induced by a determinant algorithm is introduced and studied.
In Chap. 6, we develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales and several applications are provided. In particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e., fuzzy quantum dynamic systems) is proposed and studied.

This book will establish an almost periodic theory of multidimensional fuzzy dynamic equations and fuzzy vector-valued functions on complete-closed time scales under non-translational shifts including some commonly irregular time scales, and it involves an almost periodic theory of fuzzy functions on quantum-like time scales.