Multiparameterized Hypersoft Set and Type-2 Hypersoft Set

Takaaki Fujita; Iqbal M. Batiha

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan,
Iqbal M. Batiha Department of Mathematics, Al Zaytoonah University of Jordan, Amman, Jordan, Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

Keywords:

Superhypersoft set, Soft Set, Hypersoft set, Multiparameterized Soft Set, Type-2 Soft Set

Abstract

To model real-world uncertainty, various mathematical frameworks have been proposed, including Fuzzy Sets
[78,79], HyperfuzzySets[29,34,45],IntuitionisticFuzzySets[7,8], NeutrosophicSets[66,67],PlithogenicSets
[25,68], and Rough Sets [57–59]. Soft sets provide a robust mathematical framework for decision-making by
associatingparameterswithsubsetsofauniversalset,therebyeffectivelyaddressinguncertaintyandimprecision
[46,49]. Over time, various extensions of soft sets—such as Hypersoft Sets [41], SuperHypersoft Sets [62],
and Treesoft Sets [5]—have been introduced to model increasingly complex decision-making environments.
This paper introduces and rigorously formalizes the concepts of the Multiparameterized Hypersoft Set and the
Type-2 Hypersoft Set. These models naturally extend the classical Multiparameterized Soft Set and Type-2
Soft Set, respectively, enhancing their ability to represent multi-dimensional and hierarchical uncertainty in
practical applications.

DOI: 10.5281/zenodo.17081333