412 202
Full Length Article
Volume 7 , Issue 1, PP: 55-61 , 2020

Title

A New Approach Of Neutrosophic Topological space

Authors Names :   Riad K. Al-Hamido   1 *  

1  Affiliation :  Department of Mathematics, College of Science, Al-Furat University, Deir-ez-Zor, Syria

    Email :  riad-hamido1983@hotmail.com



Doi   :  10.5281/zenodo.3876229


Abstract :

  In this paper, a new approach of neutrosophic topological space (NA-NTS) is going to be introduced which is more general than neutrosophic topological space. Moreover, a new kind of neutrosophic sets and neutrosophic concepts in this new space is going to be created, which may makes us created a new kind in neutrosophic topology. We prove that a new approach of neutrosophic topological space is not a classical topological space. Also, a new approach of neutrosophic topological space is neither neutrosophic topological space nor neutrosophic crisp topological space. Many examples and theories are presented..

 

Keywords :

 New approach of neutrosophic topological spaces , new approach of neutrosophic open sets , new approach of neutrosophic closed sets.

References :

[1]   L. A. Zadeh, "Fuzzy Sets", Inform. Control,Vol 8, pp.338-353, 1965.

[2]   K. Atanassov, "Intuitionistic Fuzzy Sets", Fuzzy Sets And Systems, Vol 20, pp.87-96, 1986.

[3]   F. Smarandache, "A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press, Rehoboth, NM, 1999.

[4]   F. Smarandache, "Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics", University of New Mexico, Gallup, NM 87301, USA 2002.

[5]   A. A.Salma, S.A. Alblowi, "Neutrosophic set and neutrosophic topological spaces", IOSR J.  Math., Vol 3, pp.31–35. 2012.

[6]   M. Abdel-Basset, M. Mai, E. Mohamed, C. Francisco, H. Z. Abd El-Nasser, "Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases", Artificial Intelligence in Medicine 101, 101735, 2019.

[7]   M. Abdel-Basset, E. Mohamed, G. Abduallah, and F. Smarandache, "A novel model for evaluation Hospital medical care systems based on plithogenic sets", Artificial intelligence in medicine Vol 100, 2019, 101710.

[8]   M. Abdel-Basset, G. Gunasekaran Mohamed, G. Abduallah, C. Victor, "A Novel Intelligent Medical Decision Support Model Based on Soft Computing and IoT" IEEE Internet of Things Journal, 2019.

[9]   M. Abdel-Basset, G. Abduallah, G. Gunasekaran, L.  Hoang Viet, "A novel group decision making model based on neutrosophic sets for heart disease diagnosis", Multimedia Tools and Applications,Vol 10, pp1-26, 2019.  

[10] R.K. Al-Hamido, "Neutrosophic Crisp Bi-Topological Spaces", Neutrosophic Sets and Systems, Vol 21, pp.66-73, 2018. 

[11]  Al-Hamido, R. K, "A study of multi-Topological Spaces", PhD Theses, AlBaath university , Syria, 2019.

[12]  A. B.AL-Nafee, R.K. Al-Hamido, F.Smarandache, "Separation Axioms In Neutrosophic Crisp Topological Spaces", Neutrosophic Sets and Systems, Vol 25, pp.25-32, 2019.

[13]  Al-Hamido, R. K, "Neutrosophic Crisp Supra Bi-Topological Spaces", International Journal of Neutrosophic  Science, Vol 1, pp.66-73, 2018. 

[14]  A.A.A. Agboola, A.D. Akinola and O.Y. Oyebola, "Neutrosophic Rings I", Int. J. of Math. Comb, Vol 4, pp.1-14, 2011.

[15]  A.A.A. Agboola, A.O. Akwu and Y.T. Oyebo, "Neutrosophic Groups and Neutrosopic Subgroups", Int. J.of Math. Comb, Vol 3, pp.1-9, 2012.

[16]  A.A.A. Agboola, "On Refined Neutrosophic Algebraic Structures",  Neutrosophic Sets and Systems, Vol 10, pp.99-101, 2015.

[17]  E.O. Adeleke,  A.A.A. Agboola and F. Smarandache, "Refined Neutrosophic Rings I", International Journal

of Neutrosophic Science (IJNS), Vol. 2, pp.77-81, 2020. 

[18]  E.O. Adeleke,  A.A.A. Agboola and F. Smarandache, "Refined Neutrosophic Rings II", International Journal

of Neutrosophic Science (IJNS), Vol. 2, pp.89-94, 2020. 

[19]  W. B. Vasantha Kandasamy, and F. Smarandache, "Neutrosophic Rings", Neutrosophic Sets and Systems, 2006.

[20]  F. Smarandache, S. Pramanik, "New Neutrosophic Sets via Neutrosophic Topological Spaces", In Neutrosophic Operational Research; Pons Editions: Brussels, Belgium, Vol 1, pp.189–209, 2017. 

[21]  W. Al-Omeri, "Neutrosophic crisp sets via neutrosophic crisp topological spaces", Neutrosophic Sets Syst, Vol 13, pp.96–104, 2016.

[22]  W. Al-Omeri, S. Jafari, "On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces", Mathematics, Vol 7, pp.1-12, 2019. doi:doi.org/10.3390/math7010001.

[23]  F. Smarandache, "n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in Physics, Vol 4, pp.143-146, 2013.