619 365
Full Length Article
International Journal of Neutrosophic Science
Volume 6 , Issue 1, PP: 08-21 , 2020 | Cite this article as | XML |PDF

Title

Single Valued Neutrosophic Filters

Authors Names :   Giorgio Nordo   1 *     Arif Mehmood   2     Said Broumi   3  

1  Affiliation :  MIFT - Department of Mathematical and Computer Science, Physical Sciences and Earth Sciences, Messina University, Italy

    Email :  giorgio.nordo@unime.it


2  Affiliation :  Department of Mathematics and Statistics, Riphah International University Sector I-14, Islamabad, Pakistan

    Email :  mehdaniyal@gmail.com


3  Affiliation :  Laboratory of Information Processing, Faculty of Science Ben M’sick, University Hassan II, Casablanca, Morocco

    Email :  broumisaid78@gmail.com



Doi   :  10.5281/zenodo.3830930


Abstract :

In this paper we give a comprehensive presentation of the notions of filter base, filter and ultrafilter on single valued neutrosophic set and we investigate some of their properties and relationships. More precisely, we discuss properties related to filter completion, the image of neutrosophic filter base by a neutrosophic induced mapping and the infimum and supremum of two neutrosophic filter bases.

 

Keywords :

neutrosophic set , single valued neutrosphic set , neutrosophic induced mapping , single valued neutrosophic filter , neutrosophic completion , single valued neutrosophic ultrafilter

References :

[1]     Al-Omeri W., Jafari S. On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces. Mathematics 7 (1), pp. 1-12. 2019.

[2]     Atanassov K.T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20 (1), pp. 87-96, 1986.

[3]     Bera T., Mahapatra N.K. Introduction to neutrosophic soft topological spaces, Opsearch (March, 2017), DOI:10.1007/s12597-017-0308-7.

[4]     Bera T., Mahapatra N.K. On neutrosophic soft topological space. Neutrosophic Sets and Systems 19 (1), pp. 3-15, 2018.

[5]     Bourbaki N. .General Topology. Springer Science and Business Media, 2020.

[6]     Broumi S., Talea M., Bakali A., Smarandache F. Single valued neutrosophic graphs. Journal of New theory 10, pp. 86-101, 2016.

[7]     Cartan H. The´orie des filtres. Comptes Rendus de l’Acade´mie des Sciences 205, pp. 595-598, 1937.

[8]     Chang C.L. Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications 24, pp. 182- 190,1968.

[9]     Coker D. An Introduction to Intuitionistic Fuzzy Topological Spaces. Fuzzy Sets and Systems 88, pp. 81-89,1997.

[10]     Engelking R. General Topology. Berlin: Heldermann Verlag, 1989.

[11]     Gemignani M.C. Elementary Topology. New York: Dover Publications Inc., 1990.

[12]     Latreche A., Barkat O., Milles S., Ismail F. Single valued neutrosophic mappings defined by single valued neutrosophic relations with applications. Neutrosophic Sets and Systems 1, pp. 203-220, 2020.

[13]     Mehmood A., Nordo G., Zamir M., Park C., Nazia H., Nadeem F., Shamona J. Soft b-separation axioms inneutrosophic soft topological structures. Annals of Fuzzy Mathematics and Informatics 18, pp. 93–105, 2019.

[14]     Mehmood A., Nadeem F., Nordo G., Zamir M., Park C., Kalsoom H., Jabeen S., Khan M.Y. Generalized neutrosophic separation axioms in neutrosophic soft topological spaces. Neutrosophic Sets and Systems 32 (1), pp. 38–51, 2020.

[15]     Parimala M., Karthika M., Smarandache F., Broumi S., On αω-closed sets and itsconnectedness in terms ofneutrosophic topological spaces, International Journal of Neutrosophic Science 2 (2), pp. 82-88, 2020.

[16]    Saber Y., Alsharari F., Smarandache F. On Single-Valued Neutrosophic Ideals in S¸ ostak Sense. Symmetry

 

12 (2):193, 2020.


Cite this Article as :
Giorgio Nordo , Arif Mehmood , Said Broumi, Single Valued Neutrosophic Filters, International Journal of Neutrosophic Science, Vol. 6 , No. 1 , pp. 08-21 , 2020 (Doi   :  10.5281/zenodo.3830930)