Hyperfunctions and Superhyperfunctions in Linear Programming:

Foundations and Applications

Takaaki Fujita1, Maisam Jdid2,3,∗, Florentin Smarandache4

1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan

22Faculty of Science, Damascus University, Damascus, Syria

33Department of Requirements, International University for Science and Technology, Ghabageb, Syrian Arab

Republic

4University of New Mexico, Mathematics, Physics, and Natural Sciences Division 705 Gurley Ave., Gallup,

NM 87301, USA

Emails: Takaaki.fujita060@gmail.com; maissam.jdid66@damascusuniversity.edu.sy; smarand@unm.edu

Abstract

A hyperfunction maps each input to a subset of outputs, generalizing classical functions to represent multi-

valued or uncertain outcomes. A superhyperfunction extends this idea further by mapping sets (or sets of sets)

to higher-order powerset values, thereby capturing complex hierarchical or layered uncertainties. In this paper,

we explore the use of hyperfunctions and superhyperfunctions in linear programming. Specifically, we ex-

amine the Linear Objective (Profit/Cost) n-SuperHyperfunction and the Linear Utility n-SuperHyperfunction.

We hope these concepts will advance both hyperfunction theory and the study of linear programming under

uncertainty.

Keywords: Hyperfunction; Superhyperfunction; Linear Programming; Linear Utility Function; Linear Objec-

tive (Profit/Cost) Function