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International Journal of Neutrosophic Science
Volume 17 , Issue 1, PP: 30-40 , 2021 | Cite this article as | XML | Html |PDF

Title

On Some Properties of Interior, Closure, Boundary and Exterior of Neutrosophic Multi Topological Space

Authors Names :   Bhimraj Basumatary   1 *     Nijwm Wary   2     Said Broumi   3  

1  Affiliation :  Department of Mathematical Sciences, Bodoland University, Kokrajhar, INDIA

    Email :  brbasumatary14@gmail.com (https://orcid.org/0000-0001-5398-6078 )


2  Affiliation :  Department of Mathematical Sciences, Bodoland University, Kokrajhar, INDIA

    Email :  nijwmwr0@gmail.com ( https://orcid.org/0000-0003-3647-0541 )


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

    Email :  broumisaid78@gmail.com (https://orcid.org/0000-0002-1334-5759 )



Doi   :   https://doi.org/10.54216/IJNS.170102

Received: September 02, 2021 Accepted: December 01, 2021

Abstract :

This paper introduced the concept of neutrosophic multi topological space. The definitions of the interior, closure, exterior, and boundary of neutrosophic multiset is defined and also, its propositions will be studied with examples. 

Keywords :

Neutrosophic Multiset , Neutrosophic Multi Topological Space , Neutrosophic Multi Exterior , Neutrosophic Multi Boundary 

References :

[1]     Zadeh, L.A. “Fuzzy sets”. Inf. Control, 8, pp.338–353, 1965.

[2]     Atanassov, K.T. “Intuitionistic fuzzy sets”. Fuzzy Sets and Systems, 20, pp.87–96, 1986.

[3]     Chang, C.L. “Fuzzy topological spaces”. J. Math. Anal. Appl., 24(1), pp.182–190, 1968.

[4]     Çoker, D. “An introduction to intuitionistic fuzzy topological spaces”. Fuzzy Sets and Systems , 88(1), pp.81–89, 1997.

[5]     Kelly, J. “Bitopological spaces”. Proc. Lond. Math. Soc., 3(1), pp.71–89, 1963.

[6]     Mwchahary, D.D. and Basumatary, B. “A note on neutrosophic bitopological spaces”. Neutrosophic Sets and Systems, 33, pp.134–144, 2020.

[7]     Smarandache, F. “Neutrosophy / Neutrosophic probability, set, and logic”. American Research Press, 1998. http://gallup.unm.edu/~smarandache/NeutLog.txt

[8]     Smarandache, F. “Neutrosophic set-a generalization of the intuitionistic fuzzy set”. Int. J. Pure Appl. Math., 24(3), pp.287–297, 2005.

[9]     Smarandache, F. “Neutrosophic perspectives: triplets, duplets, multisets, hybrid operators, modal logic, hedge algebras and applications”. Pons Editions, Bruxelles, 323, pp.115–119, 2017.

[10]   Smarandache, F. “Neutrosophy and neutrosophic logic, first international conference on neutrosophy, neutrosophic logic, set, probability, and statistics”. University of New Mexico, Gallup, NM 87301, USA, 2002.

[11]   Broumi, S., Deli, I. and Smarandache, F. “Relations on interval valued neutrosophic soft sets”. J. New Results Sci., 3(5), pp.1–20, 2014.

[12]   Broumi, S., Deli, I. and Smarandache, F. “Neutrosophic parametrized soft set theory and its decision making”. International Frontier Science Letters, 1(1), pp.1–11, 2014.

[13]   Sumathi, I.R. and Arockiarani, I. “Fuzzy neutrosophic groups”. Adv. Fuzzy Math, 10(2), pp.117–122, 2015.

[14]   Sumathi, I.R. and Arockiarani, I. Topological group structure of neutrosophic set. Journal of Advanced Studies in Topology, 7(1), pp.12–20, 2016.

[15]   Salama, A.A. and Alblowi, S.A. “Neutrosophic set and neutrosophic topological spaces”. IOSR Journal of Mathematics (IOSR-JM), 3(4), pp.31–35, 2012.

[16]   Al-Hamido, R.K. “Neutrosophic crisp bi-topological spaces”. Neutrosophic Sets and Systems, 21, pp.66–73, 2018.

[17]   Hamido, R.K. and Gharibah, T. “Neutrosophic crisp tri-topological spaces”. Journal of New Theory, (23), pp.13–21, 2018.

[18]   Devi, R., Dhavaseelan, R. and Jafari, S. “On separation axioms in an ordered neutrosophic bitopological space”. Neutrosophic Sets and Systems, 18(1), pp.27–36, 2017.

[19]   Basumatary, B. and Wary, N. “A study on neutrosophic bitopological group”. Neutrosophic Sets and Systems, (38), pp.164–178, 2020.

[20]   Basumatary, B., Wary, N., Saeed, M. and Saqlain, M. “On some properties of plithogenic neutrosophic hypersoft almost topological group”. Neutrosophc Sets and Systems, 43, pp.169–179, 2020.

[21]   Kazancı, O., Hoskova-Mayerova, S. and Davvaz, B. “Application multi-fuzzy soft sets in hypermodules”. Mathematics, 9(18), pp.2182, 2021.

[22]   Blizard, W. D. “Multiset theory”. Notre Dame Journal of formal logic, 30(1), pp.36–66, 1989.

[23]   Tella, Y. and Daniel, S. “A note on power whole multiset of a multiset and multiset topologies”. Journal of Computer and Mathematical Sciences, 5(1), pp.1–122, 2014.

[24]   Onasanya, B. O. and Hoskova-Mayerova, S. “Multi-fuzzy group induced by multisets”. Ital. J. Pure Appl. Math, 41, pp.597–604, 2019.

[25]   Al Tahan, M., Hoskova-Mayerova, S. and Davvaz, B. “Fuzzy multi-polygroups”. Journal of Intelligent & Fuzzy Systems, 38(2), pp.2337–2345, 2020.

[26]   Sebastian, S. and Ramakrishnan, T. V. “Multi-fuzzy sets: An extension of fuzzy sets”. Fuzzy Information and Engineering, 3(1), pp.35–43, 2011.

[27]   Dey, A. and Pal, M. “Multi-fuzzy complex numbers and multi-fuzzy complex sets”. International Journal of Fuzzy System Applications (IJFSA), 4(2), pp.15–27, 2015.

[28]   Uluçay, V. and Şahin, M. Neutrosophic multigroups and applications. Mathematics, 7(1), pp.95, 2019.

[29]   Basumatary, B., Wary, N., Mwchahary, D.D., Brahma, A.K., Moshahary, J., Basumatary, U.R., and Basumatary, J. “A study on some properties of neutrosophic multi topological group”. Symmetry, 13(9), pp.1689, 2021.

[30]   Basumatary, B. “Towards forming the field of fuzzy closure with reference to fuzzy boundary”. Journal of Process Management. New Technologies, 4(1), pp.30–40, 2016.


Cite this Article as :
Bhimraj Basumatary , Nijwm Wary , Said Broumi, On Some Properties of Interior, Closure, Boundary and Exterior of Neutrosophic Multi Topological Space, International Journal of Neutrosophic Science, Vol. 17 , No. 1 , (2021) : 30-40 (Doi   :  https://doi.org/10.54216/IJNS.170102)