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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Main Author: Yanna Deng
Format: Article
Language:English
Published: University of New Mexico 2025-07-01
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.
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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