A Concise Introduction to HyperFuzzy, HyperNeutrosophic,  HyperPlithogenic, HyperSoft, and HyperRough Sets with  Practical Examples

Takaaki Fujita; Florentin Smarandache

A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan.
Florentin Smarandache University of New Mexico, Gallup Campus, NM 87301, USA.

Keywords:

HyperFuzzy Set, HyperNeutrosophic Set, HyperPlithogenic Set, HyperRough Set, HyperSoft Set

Abstract

Various set concepts are widely recognized for effectively addressing u ncertainty, including fuzzy
sets, neutrosophic sets, plithogenic sets, rough sets, and soft sets. These concepts have been further extended
through hyperstructures (based on powersets) and superhyperstructures (based on n-th powersets, which are sets
with repeated power set structures) [5,12–14,32]. These extensions are commonly referred to as HyperUncertain,
SuperUncertain, and SuperHyperUncertain Sets/Logics/Probabilities/Statistics, and they were introduced by
Smarandache in 2016-2017 [32] as parts of HyperStructures, SuperStructures, and SuperHyperStructures respectively.
This paper recalls these concepts along with concrete examples.

DOI: 10.5281/zenodo.14759385

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Published

2025-03-01

Issue

Vol. 80 (2025): Neutrosophic Sets and Systems

Section

Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons Attribution (CC BY) license.

How to Cite

Takaaki Fujita, & Florentin Smarandache. (2025). A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples. Neutrosophic Sets and Systems, 80, 609-631. https://fs.unm.edu/nss8/index.php/111/article/view/5764