Volume 26 • Issue 4 • PP: 65-76 • 2025
Hyperfunctions and Superhyperfunctions in Linear Programming: Foundations and Applications
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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 examine 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.
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