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

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 approachto decision-making by mapping parameters to subsets of a universal set, thereby addressing uncertainty andvagueness in a systematic way. As an extension of soft sets, TreeSoft Sets and ForestSoft Sets have beenintroduced to incorporate hierarchical structures into soft set theory. In this paper, we further extend theTreeSoft framework and introduce three new models: the MultiTree-Soft Set, the PseudoTree-Soft Set, and theHyperTree-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 mapsvertex-subsets of a pseudotree to subsets of the universe, thereby capturing uncertainty over parameter systemsthat are “almost trees,” with at most one cycle. A HyperTree-Soft Set associates subsets of the universe withunions of hyperedges in a hypertree, effectively modeling interactions among attributes whose incidences formconnected subtrees of a host tree. These three constructions strictly generalize the existing TreeSoft Set modelwhile preserving a clear underlying graph or hypergraph structure, thus enriching the toolkit for hierarchicaland network-based soft set modeling. Furthermore, we also introduce a new concept called the Tree-to-Tree-SoftSet.