In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...

In this paper, we introduce the concept of $$\alpha $$ -fractal function and fractal approximation for a set-valued continuous map defined on closed bounded interval real numbers. Also, study some properties such functions. Further, estimate perturbation error between given its function. Additionally, define new graph different from standard introduced in literature establish bounds dimension n...