Volume 13 , Issue 1 , PP: 28-33, 2021 | Cite this article as | XML | Html | PDF | Full Length Article
Florentin Smarandache 1
Doi: https://doi.org/10.54216/IJNS.130104
In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false.
Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true.
The NeutroTheorem and AntiTheorem are generalizations and alternatives of the classical Theorem in any science.
More general, by the process of NeutroSophication, we have extended any classical Structure, in no matter what field of knowledge, to some NeutroStructure, and by the process of AntiSophication to some AntiStructure
Structure, NeutroStructure, and AntiStructure
[1] F. Smarandache: NeutroAlgebra is a Generalization of Partial Algebra. International Journal of Neutrosophic Science (IJNS), Volume 2, pp. 8-17, 2020. DOI: http://doi.org/10.5281/zenodo.3989285
http://fs.unm.edu/NeutroAlgebra.pdf
[2] F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Chapter 6, pages 240-265, 2019; http://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf
[3] Florentin Smarandache: Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited). Neutrosophic Sets and Systems, vol. 31, pp. 1-16, 2020. DOI: 10.5281/zenodo.3638232
http://fs.unm.edu/NSS/NeutroAlgebraic-AntiAlgebraic-Structures.pdf
[4] Florentin Smarandache, Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures, Journal of Fuzzy Extension and Applications (JFEA), J. Fuzzy. Ext. Appl. Vol. 1, No. 2, pp. 85–87, 2020. DOI: 10.22105/jfea.2020.248816.1008
http://fs.unm.edu/NeutroAlgebra-general.pdf
[5] A.A.A. Agboola, M.A. Ibrahim, E.O. Adeleke: Elementary Examination of NeutroAlgebras and AntiAlgebras viz-a-viz the Classical Number Systems. International Journal of Neutrosophic Science (IJNS), Volume 4, pp. 16-19, 2020. DOI: http://doi.org/10.5281/zenodo.3989530
http://fs.unm.edu/ElementaryExaminationOfNeutroAlgebra.pdf
[6] A.A.A. Agboola: Introduction to NeutroGroups. International Journal of Neutrosophic Science (IJNS), Volume 6, pp. 41-47, 2020. DOI: http://doi.org/10.5281/zenodo.3989823
http://fs.unm.edu/IntroductionToNeutroGroups.pdf
[7] A.A.A. Agboola: Introduction to NeutroRings. International Journal of Neutrosophic Science (IJNS), Volume 7, pp. 62-73, 2020. DOI: http://doi.org/10.5281/zenodo.3991389
http://fs.unm.edu/IntroductionToNeutroRings.pdf
[8] Akbar Rezaei, Florentin Smarandache: On Neutro-BE-algebras and Anti-BE-algebras. International Journal of Neutrosophic Science (IJNS), Volume 4, pp. 8-15, 2020. DOI: http://doi.org/10.5281/zenodo.3989550
http://fs.unm.edu/OnNeutroBEalgebras.pdf
[9] Mohammad Hamidi, Florentin Smarandache: Neutro-BCK-Algebra. International Journal of Neutrosophic Science (IJNS), Volume 8, pp. 110-117, 2020. DOI: http://doi.org/10.5281/zenodo.3991437
http://fs.unm.edu/Neutro-BCK-Algebra.pdf
[10] Florentin Smarandache, Akbar Rezaei, Hee Sik Kim: A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science (IJNS) Vol. 5, No. 1 , pp. 8-15, 2020; DOI: 10.5281/zenodo.3788124
http://fs.unm.edu/Neutro-CI-Algebras.pdf
[11] Florentin Smarandache: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra. Neutrosophic Sets and Systems, Vol. 33, pp. 290-296, 2020. DOI: 10.5281/zenodo.3783103
http://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf
[12] A.A.A. Agboola: On Finite NeutroGroups of Type-NG. International Journal of Neutrosophic Science (IJNS), Volume 10, Issue 2, pp. 84-95, 2020. DOI: 10.5281/zenodo.4277243, http://fs.unm.edu/IJNS/OnFiniteNeutroGroupsOfType-NG.pdf
[13] A.A.A. Agboola: On Finite and Infinite NeutroRings of Type-NR. International Journal of Neutrosophic Science (IJNS), Volume 11, Issue 2, pp. 87-99, 2020. DOI: 10.5281/zenodo.4276366, http://fs.unm.edu/IJNS/OnFiniteAndInfiniteNeutroRings.pdf
[14] A.A.A. Agboola, Introduction to AntiGroups, International Journal of Neutrosophic Science (IJNS), Vol. 12, No. 2, PP. 71-80, 2020. http://fs.unm.edu/IJNS/IntroductionAntiGroups.pdf
[15] M.A. Ibrahim and A.A.A. Agboola, Introduction to NeutroHyperGroups, Neutrosophic Sets and Systems, vol. 38, pp. 15-32, 2020. DOI: 10.5281/zenodo.4300363, http://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdf
[16] Elahe Mohammadzadeh and Akbar Rezaei, On NeutroNilpotentGroups, Neutrosophic Sets and Systems, vol. 38, pp. 33-40, 2020. DOI: 10.5281/zenodo.4300370, http://fs.unm.edu/NSS/OnNeutroNilpotentGroups3.pdf
