HyperLattice-valued and SuperHyperLattice-valued Uncertain Sets with Decision Applications

Authors

• Takaaki Fujita, Independent Researcher, Tokyo, JapanFollow
• Ajoy Kanti Das, Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, IndiaFollow
• Sankar Prasad Mondal, Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, West Bengal, IndiaFollow
• Arif Mehmood, Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, PakistanFollow
• Arkan Ghaib, Department of Information Technology, Management Technical College, Southern Technical University, Basrah, 61004, IraqFollow

Authors' ORCIDs

Takaaki Fujita: https://orcid.org/0000-0002-9380-386X

Ajoy Kanti Das: https://orcid.org/0000-0002-9326-1677

Sankar Prasad Mondal: https://orcid.org/0000-0003-4690-2598

Arif Mehmood: https://orcid.org/0000-0002-6230-9236

Arkan Ghaib: https://orcid.org/0009-0001-3355-0880

Article Type

Research Article

Abstract

Fuzzy set theory enriches classical sets by assigning to each element a graded membership in [0,1], thereby capturing partial inclusion and uncertainty. The notion of an Uncertain Set further abstracts this idea by allowing membership to take values in a general degree-domain, providing a unified language that subsumes fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and related models. On the algebraic side, a hyperlattice replaces one lattice operation by a multivalued hyperoperation, enabling the representation of ambiguous or non-deterministic combinations, while a superhyperlattice iterates this structure through powerset lifting to obtain higher-order layers of interaction. Motivated by these developments, we introduce HyperLattice-valued and SuperHyperLattice-valued Uncertain Sets as lattice-valued uncertainty frameworks whose degrees range over hyperlattices and their superextensions. We establish basic definitions, show that the proposed formalisms generalize existing lattice-valued models (including L-fuzzy, L-neutrosophic, and L-plithogenic sets), and discuss fundamental structural properties and canonical embeddings between the resulting classes.

Keywords

Hyperlattice, Fuzzy set, Neutrsophic set, L-fuzzy set, SuperHyperLattice, Uncertain set

How to Cite

Fujita, Takaaki; Das, Ajoy Kanti; Mondal, Sankar Prasad; Mehmood, Arif; and Ghaib, Arkan (2026) "HyperLattice-valued and SuperHyperLattice-valued Uncertain Sets with Decision Applications," Neutrosophic Systems with Applications: Vol. 26: Iss. 8, Article 1. DOI: https://doi.org/10.63689/2993-7159.1357