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

Various set concepts are widely recognized for effectively a ddressing u ncertainty, i ncluding 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 p...

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Main Authors: Florentin Smarandache, Takaaki Fujita
Format: Article
Language:English
Published: University of New Mexico 2025-04-01
Series:Neutrosophic Sets and Systems
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Online Access:https://fs.unm.edu/NSS/37HyperFuzzy.pdf
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author Florentin Smarandache
Takaaki Fujita
author_facet Florentin Smarandache
Takaaki Fujita
author_sort Florentin Smarandache
collection DOAJ
description Various set concepts are widely recognized for effectively a ddressing u ncertainty, i ncluding 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.
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series Neutrosophic Sets and Systems
spelling doaj-art-7839b82ee3b448f49451998026bd337a2025-08-25T10:26:53ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-04-018060963110.5281/zenodo.14759385A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical ExamplesFlorentin SmarandacheTakaaki FujitaVarious set concepts are widely recognized for effectively a ddressing u ncertainty, i ncluding 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. https://fs.unm.edu/NSS/37HyperFuzzy.pdfhyperfuzzy sethyperneutrosophic sethyperplithogenic sethyperrough sethypersoft set
spellingShingle Florentin Smarandache
Takaaki Fujita
A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
Neutrosophic Sets and Systems
hyperfuzzy set
hyperneutrosophic set
hyperplithogenic set
hyperrough set
hypersoft set
title A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
title_full A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
title_fullStr A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
title_full_unstemmed A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
title_short A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
title_sort concise introduction to hyperfuzzy hyperneutrosophic hyperplithogenic hypersoft and hyperrough sets with practical examples
topic hyperfuzzy set
hyperneutrosophic set
hyperplithogenic set
hyperrough set
hypersoft set
url https://fs.unm.edu/NSS/37HyperFuzzy.pdf
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