NeutroAlgebra & AntiAlgebra vs. Classical Algebra
Subject Areas : Transactions on Fuzzy Sets and Systems
Florentin Smarandache
1
(Department of Mathematics, Physics, and Natural Science, University of New Mexico, New Mexico State 87301, USA.)
Keywords: NeutroAlgebra, AntiAlgebra, NeutroOperation, NeutroAxiom, AntiAxiom, Classical Algebra, AntiOperation.,
Abstract :
NeutroAlgebra & AntiAlgebra vs. Classical Algebra is a like Realism vs. Idealism. Classical Algebra does not leave room for partially true axioms nor partially well-defined operations. Our world is full of indeterminate (unclear, conflicting, unknown, etc.) data. This paper is a review of the emerging, development, and applications of the NeutroAlgebra and AntiAlgebra [2019-2022] as generalizations and alternatives of classical algebras.
[1] A. A. A. Agboola, Introduction to NeutroGroups, Int. J. Neutrosophic Sci., 6 (2020), 41-47. Available online: http://fs.unm.edu/IntroductionToNeutroGroups.pdf.
[2] A. A. A. Agboola, Introduction to NeutroRings, Int. J. Neutrosophic Sci., 7 (2020), 62-73. Available online: http://fs.unm.edu/IntroductionToNeutroRings.pdf.
[3] A. A. A. Agboola, On Finite NeutroGroups of Type-NG, Int. J. Neutrosophic Sci., 10 (2020), 84-95. Available online: http://fs.unm.edu/IJNS/OnFiniteNeutroGroupsOfType-NG.pdf.
[4] A. A. A. Agboola, On Finite and Infinite NeutroRings of Type-NR, Int. J. Neutrosophic Sci., 11 (2020), 87-99. Available online: http://fs.unm.edu/IJNS/OnFiniteAndInfiniteNeutroRings.pdf.
[5] A. A. A. Agboola, Introduction to AntiGroups, Int. J. Neutrosophic Sci., 12(2) (2020), 71-80, http://fs.unm.edu/IJNS/IntroductionAntiGroups.pdf.
[6] A. A. A. Agboola, M. A. Ibrahim and E.O. Adeleke, Elementary Examination of NeutroAlgebras and AntiAlgebras viz-a-viz the Classical Number Systems, Int. J. Neutrosophic Sci., 4 (2020), 16-19. Available online: http://fs.unm.edu/ElementaryExaminationOfNeutroAlgebra.pdf.
[7] M. Al-Tahan, NeutroOrderedAlgebra: Theory and Examples, 3rd International Workshop on Advanced Topics in Dynamical Systems, University of Kufa, Kufa, Iraq, (2021).
[8] M. Al-Tahan, B. Davvaz, F. Smarandache and O. Anis, On Some NeutroHyperstructures, Symmetry, 13 (2021), 1-12. Available online: http://fs.unm.edu/NeutroHyperstructure.pdf.
[9] M. Al-Tahan, F. Smarandache and B. Davvaz, NeutroOrderedAlgebra: Applications to Semigroups, Neutrosophic Sets and Syst. 39 (2021), 133-147, DOI: 10.5281/zenodo.4444331.
[10] M. Hamidi and F. Smarandache, Neutro-BCK-Algebra, Int. J. Neutrosophic Sci., 8 (2020), 110-117. Available online: http://fs.unm.edu/Neutro-BCK-Algebra.pdf.
[11] M. A. Ibrahim and A. A. A. Agboola, Introduction to NeutroHyperGroups, Neutrosophic Sets Syst., 38 (2020), 15-32. Available online: http://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdf.
[12] D. S. Jimenez, J. A. V. Mayorga, M. E. R. Ubilla and N. B. Hernandez, NeutroAlgebra for the evaluation of barriers to migrants’access in Primary Health Care in Chile based on PROSPECTOR function, Neutro sophic Sets Syst., 39 (2021), 1-9. DOI: 10.5281/zenodo.4444189.
[13] E. Mohammadzadeh and A. Rezaei, On NeutroNilpotentGroups, Neutrosophic Sets Syst., 38 (2020), 33-40. Available online: http://fs.unm.edu/NSS/OnNeutroNilpotentGroups3.pdf.
[14] A. Rezaei and F. Smarandache, On Neutro-BE-algebras and Anti-BE-algebras, Int. J. Neutrosophic Sci., 4 (2020), 8-15. Available online: http://fs.unm.edu/OnNeutroBEalgebras.pdf.
[15] A. Rezaei, F. Smarandache and S. Mirvakili, Applications of (Neutro/Anti)sophications to Semihyper groups, Journal of Mathematics, Hindawi, (2021), 1-7. https://doi.org/10.1155/2021/6649349.
[16] F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, Pons Publishing House Brussels, Belgium, (2019), 240-265. Available online: http://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf.
[17] F. Smarandache, Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic Structures, J. Fuzzy. Ext. Appl., 1(2) (2020), 85–87. Available online: http://fs.unm.edu/NeutroAlgebra-general.pdf.
[18] F. Smarandache, NeutroAlgebra is a Generalization of Partial Algebra, Int. J. Neutrosophic Sci., 2 (2020), 8-17. Available online: http://fs.unm.edu/NeutroAlgebra.pdf.
[19] F. Smarandache, Structure, NeutroStructure, and AntiStructure in Science, Int. J. Neutrosophic Sci., 13 (2020), 28-33. Available online: http://fs.unm.edu/IJNS/NeutroStructure.pdf.
[20] F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited), Neutrosophic Sets Syst., 31 (2020), 1-16. Available online: http://fs.unm.edu/NSS/NeutroAlgebraic- AntiAlgebraic-Structures.pdf.
[21] F. 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 Syst., 33 (2020), 290-296. Available online: http://fs.unm.edu/NSS/n- SuperHyperGraph-n-HyperAlgebra.pdf.
[22] F. Smarandache, Universal NeutroAlgebra and Universal AntiAlgebra, Educational Publ., Grandview Heights, OH, United States, (2021).
[23] F. Smarandache, A. Rezaei, A. A. A. Agboola, Y. B. Jun, R. A. Borzooei, B. Davvaz, A. Broumand Saeid, M. Akram, M. Hamidi and S. Mirvakilii, On NeutroQuadrupleGroups, 51st Annual Mathematics Conference, February, Kashan, Iran, (2021), 16-19.
[24] F. Smarandache, A. Rezaei and H. S. Kim, A New Trend to Extensions of CI-algebras, Int. J. Neutrosophic Sci., 5 (2020), 8-15. Available online: http://fs.unm.edu/Neutro-CI-Algebras.pdf.