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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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-04-01
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| 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. |
| format | Article |
| id | doaj-art-7839b82ee3b448f49451998026bd337a |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of New Mexico |
| record_format | Article |
| 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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