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Erschienen in:
2021 | OriginalPaper | Buchkapitel
1. Calculus of Fuzzy Functions
verfasst von : Svetlin G. Georgiev
Erschienen in: Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales
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Abstract
In this chapter are introduced new classes of delta derivatives called first type fuzzy delta derivative and second type fuzzy delta derivative. Their existence and uniqueness are proved. Some of their basic properties such as fuzzy delta differentiation of a sum of two fuzzy functions and fuzzy delta differentiation of a multiplication of a fuzzy function with a constant are deducted. α-levels of fuzzy functions are defined, and formulae for their fuzzy delta derivatives are given. In the chapter are defined six types of multiplication of fuzzy functions, and for each type a formula for its fuzzy delta derivative is deducted. First type fuzzy delta integration and second type fuzzy delta integration of fuzzy functions are defined, and some of their basic properties are deducted. Shift operators are investigated, and complete-closed time scales under non-translational shifts are introduced. Shift almost periodic fuzzy functions are defined, and some of their properties are given.