The rank order of the neutrosophic triplets (T, I, F) may change after normalization
This paper examines the effects of normalization on the ranking order of single-valued neutrosophic triplets. Neutrosophic triplets are often normalized so that their sum equals one. However, we demonstrate that the ranking order of these triplets, when determined by score, accuracy, and certainty f...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-12-01
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| Series: | International Journal of Research in Industrial Engineering |
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| Online Access: | https://www.riejournal.com/article_209046_1124bb2a9deefdab15a8d9374d56afdf.pdf |
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| _version_ | 1832577740496175104 |
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| author | Florentin Smarandache |
| author_facet | Florentin Smarandache |
| author_sort | Florentin Smarandache |
| collection | DOAJ |
| description | This paper examines the effects of normalization on the ranking order of single-valued neutrosophic triplets. Neutrosophic triplets are often normalized so that their sum equals one. However, we demonstrate that the ranking order of these triplets, when determined by score, accuracy, and certainty functions, can change upon normalization. Through formal proofs and illustrative counter-examples, we show that inequalities between unnormalized triplets do not always hold after normalization, affecting ranking stability. These findings highlight the importance of considering normalization's impact when using neutrosophic triplets for decision-making and uncertainty modeling. |
| format | Article |
| id | doaj-art-514b3bfca2f8499a972a9c8fae5f4147 |
| institution | Kabale University |
| issn | 2783-1337 2717-2937 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | International Journal of Research in Industrial Engineering |
| spelling | doaj-art-514b3bfca2f8499a972a9c8fae5f41472025-01-30T15:10:43ZengAyandegan Institute of Higher Education,International Journal of Research in Industrial Engineering2783-13372717-29372024-12-0113442743510.22105/riej.2024.487239.1489209046The rank order of the neutrosophic triplets (T, I, F) may change after normalizationFlorentin Smarandache0University of New Mexico, Mathematics, Physics, and Natural Science Division, 705 Gurley Ave., Gallup, NM 87301, USA.This paper examines the effects of normalization on the ranking order of single-valued neutrosophic triplets. Neutrosophic triplets are often normalized so that their sum equals one. However, we demonstrate that the ranking order of these triplets, when determined by score, accuracy, and certainty functions, can change upon normalization. Through formal proofs and illustrative counter-examples, we show that inequalities between unnormalized triplets do not always hold after normalization, affecting ranking stability. These findings highlight the importance of considering normalization's impact when using neutrosophic triplets for decision-making and uncertainty modeling.https://www.riejournal.com/article_209046_1124bb2a9deefdab15a8d9374d56afdf.pdfneutrosophic setranking functionsscore functionaccuracy functiondecision-makingrank order consistency |
| spellingShingle | Florentin Smarandache The rank order of the neutrosophic triplets (T, I, F) may change after normalization International Journal of Research in Industrial Engineering neutrosophic set ranking functions score function accuracy function decision-making rank order consistency |
| title | The rank order of the neutrosophic triplets (T, I, F) may change after normalization |
| title_full | The rank order of the neutrosophic triplets (T, I, F) may change after normalization |
| title_fullStr | The rank order of the neutrosophic triplets (T, I, F) may change after normalization |
| title_full_unstemmed | The rank order of the neutrosophic triplets (T, I, F) may change after normalization |
| title_short | The rank order of the neutrosophic triplets (T, I, F) may change after normalization |
| title_sort | rank order of the neutrosophic triplets t i f may change after normalization |
| topic | neutrosophic set ranking functions score function accuracy function decision-making rank order consistency |
| url | https://www.riejournal.com/article_209046_1124bb2a9deefdab15a8d9374d56afdf.pdf |
| work_keys_str_mv | AT florentinsmarandache therankorderoftheneutrosophictripletstifmaychangeafternormalization AT florentinsmarandache rankorderoftheneutrosophictripletstifmaychangeafternormalization |