Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales

Abstract

In this paper, we establish an embedding theorem for the fuzzy multidimensional space and introduce the new types of multiplications of fuzzy vectors determined by the determinant algorithm. Then some fundamental results of calculus of fuzzy vector-valued functions on time scales are established. Based on these results, we introduce the concept of shift almost periodic fuzzy vector-valued functions and develop a theory of almost periodic fuzzy functions on time scales. This function theory can be used to study almost periodic fuzzy dynamic equations on time scales including a new type of fuzzy dynamic equations called fuzzy q-dynamic equation (i.e., quantum fuzzy dynamic equation).