(T, I, F)-Neutrosophic Structures

Abstract:

In this paper we introduce for the first time a new type of structures, called (T, I, F)-Neutrosophic Structures, presented from a neutrosophic logic perspective, and we show particular cases of such structures in geometry and in algebra.

• Periodical: Applied Mechanics and Materials (Volume 811)
• Pages: 104-109
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.811.104
• Online since: November 2015
• Authors: Florentin Smarandache*
• Keywords: Algebraic Structures, Indeterminacy, Neutrosophic Axiom, Neutrosophic Bi-Algebraic Structures, Neutrosophic Geometry, Neutrosophic Groupoid, Neutrosophic Logic, Neutrosophic N-Algebraic Structures, Neutrosophic Structures, Neutrosophy

References

[1] A. Salama & Florentin Smarandache, Neutrosophic Crisp Set Theory, Educational Publisher, Columbus, Ohio, USA, 163 p., (2015).

[2] Florentin Smarandache, Neutrosophic Theory and its Applications, Collected Papers, Vol. I, EuropaNova, Brussels, Belgium, 480 p., (2014).

[3] Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, New Research on Neutrosophic Algebraic Structures, EuropaNova, Brussels, Belgium, 333 p., (2014).

[4] Florentin Smarandache, Law of Included Multiple-Middle & Principle of Dynamic Neutrosophic Opposition, EuropaNova & Educational Publisher, Brussels, Belgium – Columbus, Ohio, USA, 136 p., (2014).

DOI: 10.2139/ssrn.2731550

[5] Florentin Smarandache, Stefan Vladutescu (coordinators), Communication Neutrosophic Routes, Educational Publisher, Columbus, Ohio, USA, 217 p., (2014).

[6] F. Smarandache, Introduction to Neutrosophic Statistics, Sitech and Education Publisher, Craiova, Romania - Educational Publisher, Columbus, Ohio, USA, 123 p., (2014).

[7] Florentin Smarandache, Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability, Sitech & Educational Publisher, Craiova, Romania - Columbus, Ohio, USA, 140 p., (2013).

[8] W. B. Vasantha Kandasamy, Florentin Smarandache, Neutrosophic Interval Bialgebraic Structures, Zip Publishing, Columbus, Ohio, USA, 195 p., (2011).

[9] W.B. Vasantha Kandasamy, F. Smarandache, K, Ilanthenral, New Classes of Neutrosophic Linear Algebras, CuArt, Slatina, Romania, 286 p., (2010).

[10] Florentin Smarandache (editor), Multispace&Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV, North-European Scientific Publishers, Hanko, Finland, 800 p., (2010).

[11] F. Smarandache, V. Christianto, Neutrosophic Logic, Wave Mechanics, and Other Stories (Selected Works: 2005-2008), Kogaion Editions, Bucharest, Romania, 129 p., (2009).

[12] W. B. Vasantha Kandasamy, Florentin Smarandache, N-Algebraic Structures and S-N-Algebraic Structures, Hexis, Phoenix, Arizona, USA, 209 p., (2006).

[13] Florentin Smarandache, D. Rabounski, L. Borissova, Neutrosophic Methods in General Relativity, Hexis, Phoenix, Arizona, USA, 78 p., 2005. - Russian translation D. Rabounski, Нейтрософские методы в Общей Теории Относительности, Hexis, Phoenix, Arizona, USA, 105 p., (2006).

[14] Florentin Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, American Research Press, Rehoboth, USA, 105 p., 1998. - Republished in 2000, 2003, 2005, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics (second, third, and respectively fourth edition), American Research Press, USA, 156 p.; - Chinese translation by F. Liu, Xiquan Chinese Branch, 121 p., 2003; Сущность нейтрософии, Russian partial translation by D. Rabounski, Hexis, Phoenix, Arizona, USA, 32 p., (2006).

DOI: 10.3390/sym11040515

[15] Florentin Smarandache & Mumtaz Ali - editors, Neutrosophic Sets and Systems, book series, Vol. 1-7, Educational Publisher, Columbus, Ohio, USA, 2013-(2015).

[16] S. Bhattacharya, A Model to the Smarandache Geometries, in Journal of Recreational Mathematics", Vol. 33, No. 2, p.66, 2004-2005; - modified version in "Octogon Mathematical Magazine, Vol. 14, No. 2, pp.690-692, October (2006).

[17] S. Chimienti and M. Bencze, Smarandache Paradoxist Geometry, in Bulletin of Pure and Applied Sciences, Delhi, India, Vol. 17E, No. 1, 123-1124, 1998; http: /www. gallup. unm. edu/~smarandache/prd-geo1. txt.

[18] Linfan Mao, An introduction to Smarandache geometries on maps, presented at 2005 International Conference on Graph Theory and Combinatorics, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China, June 25-30, (2005).

[19] H. Iseri, Smarandache Manifolds, Am. Res. Press, 2002, http: /www. gallup. unm. edu/ ~smarandache /Iseri-book1. pdf.

[20] Florentin Smarandache, n-Valued Refined Neutrosophic Logic and Its Applications in Physics, Progress in Physics, USA, 143-146, Vol. 4, (2013).

[21] http: /fs. gallup. unm. edu/neutrosophy. htm; http: /fs. gallup. unm. edu/geometries. htm.