Note of HyperNeutrosophic Crisp Set and SuperHyperNeutrosophic Crisp  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,

Keywords:

Set Theory, SuperhyperNeutrosophic set, Neutrosophic Set, HyperNeutrosophic set, Neutrosophic Crisp Set

Abstract

The Neutrosophic Set provides a flexible mathematical framework for addressing uncertainty through three
distinct membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic
Set and the SuperHyperneutrosophic Set have recently been introduced to address increasingly complex
and multidimensional problems. Detailed formal definitions of these concepts can be found in [1]. A
Neutrosophic Crisp Set partitions a universe into three subsets, explicitly representing truth, indeterminacy,
and falsity memberships. In this paper, we explore the properties of the HyperNeutrosophic Crisp Set and the
SuperHyperNeutrosophic Crisp Set. These structures merge the ideas of Neutrosophic Crisp Sets with those
of Hyperneutrosophic and SuperHyperneutrosophic Sets. We anticipate that this integrated framework will
contribute to the advancement of research in areas such as Uncertain Sets and Uncertain Topology.

DOI: 10.5281/zenodo.17102620