190 114
Full Length Article
Volume 12 , Issue2, PP: 96-104 , 2020

Title

Completeness and Compactness in Standard Single Valued Neutrosophic Metric Spaces

Authors Names :   Soheyb Milles   1     Abdelkrim Latrech   2     Omar Barkat   3  

1  Affiliation :  Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of Msila, Algeria

    Email :  soheyb.milles@univ-msila.dz


2  Affiliation :  Department of Technology, Faculty of Technology, University of Skikda, Algeria

    Email :  a.latreche@univ-skikda.dz


3  Affiliation :  Laboratory of Pure and Applied Mathematics, University of Msila, Algeria

    Email :  omar.bark@gmail.com



Doi   :  10.5281/zenodo.4280977

Received: July 27, 2020 Accepted: November 15, 2020

Abstract :

 

In a recent paper, we have introduced the notion of standard single valued neutrosophic metric space as a generalization of standard fuzzy metric spaces given by J.R. Kider and Z.A. Hussain. In this paper, we continue our previous work by introducing the notions of complete standard single valued neutrosophic metric space and compact standard single valued neutrosophic metric space. Furthermore, we give a number of properties and characterizations of these notions and relationship between them.

 

Keywords :

 

Single valued neutrosophic set , Metric space , Completeness , Compactness.

 

References :

 

[1]  Atanassov, K., ”Intuitionistic fuzzy sets”, VII ITKRs Scientific Session, Sofia, 1983.

 

[2]  Guo, Y., Cheng, H.D., ” New neutrosophic approach to image segmentation”, Pattern Recognition, Vol 42, pp. 587–595, 2009.

 

[3]  Kider, J.R., Hussain, Z.A., ”Continuous and uniform continuous mappings on a standard fuzzy metric spaces”, Eng. and Tech. Journal, , Vol 32(6), pp. 1111–1119, 2014.

 

[4]   Kiris¸ci, M., S¸ims¸ek, N., ”Neutrosophic metric spaces. Mathematical Sciences”, Vol 14, pp. 241—248, 2020.

 

[5]  Latreche, A., Barkat, O., Milles, S., Ismail, F., ”Single valued neutrosophic mappings defined by single valued neutrosophic relations with applications”, Neutrosophic Sets and Systems, Vol 3, pp. 203—220, 2020.

 

[6]  Mondal, K., Pramanik, S., ”A study on problems of Hijras in West Bengal based on neutrosophic cognitive maps”, Neutrosophic Sets and Systems, Vol 5, pp. 21–26, 2014.

 

[7]  Pramanik, S., Mondal, K., ”Weighted fuzzy similarity measure based on tangent function and its application to medical diagnosis”, International Journal of Innovative Research in Science, Engineering and Technology, Vol 4, pp. 158–164, 2015.

 

[8]  Sahin, M., Kargıin, A., Yucel, M., ”Neutrosophic Triplet Partial ¨ g-Metric Spaces”Neutrosophic Sets and Systems, Vol 33, pp. 116–134, 2020.

 

[9]  Sahin, M., Kargın, A., Uz, M.S., ”Neutrosophic Triplet Partial Bipolar Metric Spaces”, Neutrosophic Sets and Systems, Vol 33, pp. 297–313, 2020

 

[10]   Smarandache, F., ”In: Neutrosophy. Neutrisophic Property, Sets, and Logic”, American Research Press. Rehoboth. USA, 1998.

 

[11]   Smarandache, F., ”In: A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set”,Neutrosophic Probability and Statistics. InfoLearnQuest, USA, 2007.

 

[12]   Smarandache, F., ” n-valued refined neutrosophic logic and its applications to Physics”, Progress in Physics, Vol 8, pp. 143–146, 2013.

 

[13]   Smarandache, F.; Pramanik, S., ”New Trends in Neutrosophic Theory and Applications”, Pons Editions, Brussels, 2016.

 

[14]   Tas¸, F., Topal, S., Smarandache, F., ” Clustering Neutrosophic Data Sets and Neutrosophic Valued Metric Spaces”, Symmetry, Vol 10, pp. 1–12, 2018.

 

[15]   Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R., ”Single valued neutrosophic sets”, Multispace Multistruct, Vol 4, pp. 410–413, 2010.

 

[16]   Yang, H.L., Guo, Z.L., Liao, X., ”On single valued neutrosophic relations”, Journal of Intelligent and Fuzzy Systems, Vol 30, 1045–1056, 2016.

 

[17]   Ye, J., ”Improved correlation coefficients of single-valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making”, Journal of Intelligent and Fuzzy Systems, Vol 27, pp. 2453– 2462, 2014.

 

[18]   Zadeh, L.A., ”Fuzzy set”, Information and Control, Vol 8, pp. 331–352, 1965