MultiTree-Soft, PseudoTree-Soft Set, HyperTree-Soft, andTree-to-Tree-Soft Set

Resumen

Various mathematical frameworks have been developed to handle uncertainty, including the con-
cepts of fuzzy sets and neutrosophic sets. Among these, soft sets provide a powerful and flexible approach
to decision-making by mapping parameters to subsets of a universal set, thereby addressing uncertainty and
vagueness in a systematic way. As an extension of soft sets, TreeSoft Sets and ForestSoft Sets have been
introduced to incorporate hierarchical structures into soft set theory. In this paper, we further extend the
TreeSoft framework and introduce three new models: the MultiTree-Soft Set, the PseudoTree-Soft Set, and the
HyperTree-Soft Set. A MultiTree-Soft Set assigns subsets of the universe to vertices or vertex-subsets of a mul-
titree, explicitly respecting its directed acyclic structure and dependency paths. A PseudoTree-Soft Set maps
vertex-subsets of a pseudotree to subsets of the universe, thereby capturing uncertainty over parameter systems
that are “almost trees,” with at most one cycle. A HyperTree-Soft Set associates subsets of the universe with
unions of hyperedges in a hypertree, effectively modeling interactions among attributes whose incidences form
connected subtrees of a host tree. These three constructions strictly generalize the existing TreeSoft Set model
while preserving a clear underlying graph or hypergraph structure, thus enriching the toolkit for hierarchical
and network-based soft set modeling. Furthermore, we also introduce a new concept called the Tree-to-Tree-Soft
Set.