Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development
This paper presents a new mathematical model called the Spherical Neutrosophic Projection Transform (SNPT). The model is based on spherical neutrosophic numbers, which represent logical states using three values: truth ( t ), indeterminacy ( i ), and falsehood ( f ). These values follow the rule 𝑡 2...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-07-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/48SphericalNeutrosophic.pdf |
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| author | Yanna Deng |
| author_facet | Yanna Deng |
| author_sort | Yanna Deng |
| collection | DOAJ |
| description | This paper presents a new mathematical model called the Spherical Neutrosophic Projection Transform (SNPT). The model is based on spherical neutrosophic numbers, which represent logical states using three values: truth ( t ), indeterminacy ( i ), and falsehood ( f ). These values follow the rule 𝑡 2 + 𝑖 2 + 𝑓 2 ≤ 3. We define a special transform that maps each triplet to another point inside the same space. This allows us to study how knowledge or beliefs change over time in uncertain systems. We prove that the transform is mathematically safe, bounded, and stable. We also create a system of differential equations that describes how the three components interact dynamically. These tools allow us to model systems where understanding, confusion, and errors change step by step. To show a real application, we use this model to track the learning progress of students in basic education. Each student's knowledge is modeled as a changing neutrosophic triplet. The results show that our model can describe how digital transformation in education affects learning quality in a measurable and logical way. This work gives a new way to connect neutrosophic mathematics with educational improvement in the digital age. |
| format | Article |
| id | doaj-art-bb65768c3c534e75b4161e8d72aaf566 |
| institution | DOAJ |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-bb65768c3c534e75b4161e8d72aaf5662025-08-20T03:07:32ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-07-018874975910.5281/zenodo.15843774Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality DevelopmentYanna DengThis paper presents a new mathematical model called the Spherical Neutrosophic Projection Transform (SNPT). The model is based on spherical neutrosophic numbers, which represent logical states using three values: truth ( t ), indeterminacy ( i ), and falsehood ( f ). These values follow the rule 𝑡 2 + 𝑖 2 + 𝑓 2 ≤ 3. We define a special transform that maps each triplet to another point inside the same space. This allows us to study how knowledge or beliefs change over time in uncertain systems. We prove that the transform is mathematically safe, bounded, and stable. We also create a system of differential equations that describes how the three components interact dynamically. These tools allow us to model systems where understanding, confusion, and errors change step by step. To show a real application, we use this model to track the learning progress of students in basic education. Each student's knowledge is modeled as a changing neutrosophic triplet. The results show that our model can describe how digital transformation in education affects learning quality in a measurable and logical way. This work gives a new way to connect neutrosophic mathematics with educational improvement in the digital age. https://fs.unm.edu/NSS/48SphericalNeutrosophic.pdfspherical neutrosophic numbersprojection transforminternal evolutiontruth-indeterminacy-falsehoodneutrosophic dynamicsbounded logicmathematical modeling |
| spellingShingle | Yanna Deng Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development Neutrosophic Sets and Systems spherical neutrosophic numbers projection transform internal evolution truth-indeterminacy-falsehood neutrosophic dynamics bounded logic mathematical modeling |
| title | Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development |
| title_full | Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development |
| title_fullStr | Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development |
| title_full_unstemmed | Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development |
| title_short | Spherical Neutrosophic Projection Transform: Modeling Knowledge Evolution in Digital Transformation for Basic Education High-Quality Development |
| title_sort | spherical neutrosophic projection transform modeling knowledge evolution in digital transformation for basic education high quality development |
| topic | spherical neutrosophic numbers projection transform internal evolution truth-indeterminacy-falsehood neutrosophic dynamics bounded logic mathematical modeling |
| url | https://fs.unm.edu/NSS/48SphericalNeutrosophic.pdf |
| work_keys_str_mv | AT yannadeng sphericalneutrosophicprojectiontransformmodelingknowledgeevolutionindigitaltransformationforbasiceducationhighqualitydevelopment |