1
Department of Mathematics, Annamalai University, Annamalainagar, Tamilnadu, India
(sksimbuking@gmail.com)
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, India
(udhayaram.v@gmail.com)
3
Department of Math and Sciences, University of New Mexico, Gallup, NM, USA
(smarand@unm.edu)
4
Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco and Regional Center for the Professions of Education and Training (C.R.M.E.F), Casablanca, Morocco
(broumisaid78@gmail.com)
Abstract :
The mathematical operations of convergence, association, supplement, arithmetical total, logarithmic item,
scalar increase, and exponentiation are the main topics of this article. We show certain important logarithmic
features of idempotency, commutativity, associativity, retention, distributivity, and De Morgan’s laws over the
addition of Neutrosophic fuzzy sets. We also outline new fixations and NFS widening and show some concepts
in action. Last but not least, we define a further operation (@)on Neutrosophic fuzzy sets and investigate
distributive laws for the case where the responsibilities of ⊕, ⊗, ∪, and ∩ are combined.
Keywords :
Neutrosophic fuzzy set; Algebraic sum; Algebraic product; Scalar multiplication and Exponentiation
operations; Intuitionistic fuzzy set.
References :
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Syst, vol. 20, no. 1, pp. 87-96, 1986.
[2] K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy set and Systems, vol.
61, pp. 137-142, 1994.
[3] K. T. Atanassov, An equality between intuitionistic fuzzy sets, Fuzzy Sets Syst, vol. 79, pp. 257-258,
1996.
[4] S. K. De, R. Biswas and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy
Sets Syst, vol. 117, no. 2, pp. 209-213, 2001.
[5] V. Cetkin, B. Pazar Varol and H. Aygun, An algebraic perspective on neutrosophic sets: fields and linear
spaces, Journal of Linear and Topological Algebra, vol. 10, no. 3, pp. 187-198, 2021.
[6] S. Das, B. K. Roy, and M. B. Kar. et al., Neutrosophic fuzzy set and its application in decision making, J
Ambient Intell Human Comput, vol. 11, pp. 5017–5029, 2020.
[7] H. Nancy Garg, Single-valued neutrosophic Entropy of order alpha, Neutrosophic Sets Syst, vol. 14, pp.
21–28, 2016a.
[8] U. Rivieccio, Neutrosophic logics: prospects and problems, Fuzzy Sets Syst, vol. 159, pp. 1860–1868,
2008.
[9] F. A. Smarandache, Unifying Field in Logics. Neutrosophy :Neutrosophic Probability, Set and Logic,
Rehoboth: American Research Press, 1999.
[10] F. Smarandache, Neutrosophy. / Neutrosophic Probability, Set, and Logic, ProQuest Information &
Learning, Ann Arbor, Michigan, USA, vol. 105, 1998.
[11] F. Smarandache, Neutrosophic set—a generalization of the intuitionistic fuzzy set, Int J Pure Appl Math,
vol. 24, no. 3, pp. 287–297, 2005.
[12] D. Stanujkic, E. K. Zavadskas, F. Smarandache, Brauers, WKM and D. A. Karabasevic, Neutrosophic
extension of the MULTIMOORA method, Informatica, vol. 28, no. 1, pp. 181–192, 2017.
[13] R. K. Verma and B. D. Sharma, Intuitionistic fuzzy sets: Some new results, Notes on Intuitionistic fuzzy
sets, vol. 17, no. 3, pp. 1-10, 2011.
[14] H.Wang, F. Smarandache, Y. Q. Zhang and R. Sunderraman, Single valued neutrosophic sets, Multispace
Multistruct, 4 (2010), 410–413.
[15] Z. Xu, J. Chen and J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Inf. Sci, vol. 178, no. 19, pp.
3775-3790, 2008.
[16] Z. Xu and X. Cai, Recent advances in intuitionistic fuzzy information aggregation, Fuzzy Optim. Decis.
Mak, vol. 9, no. 4, pp. 359-381, 2010.
[17] J. Ye, Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic
environment, Int J Gen Syst, vol. 42, no. 4, pp. 386–394, 2013.
[18] L. A. Zadeh, Fuzzy sets, Inf Control, vol. 8, pp. 338–353, 1965.
[19] L. A. Zadeh, Probability Measures of Fuzzy Events, Journal of Mathematical Analysis and Applications,
vol. 23, pp. 421-427, 1968.
| Style | # |
|---|---|
| MLA | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi. "Some Algebraic structures of Neutrosophic fuzzy sets." International Journal of Neutrosophic Science, Vol. 19, No. 2, 2022 ,PP. 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |
| APA | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi. (2022). Some Algebraic structures of Neutrosophic fuzzy sets. Journal of International Journal of Neutrosophic Science, 19 ( 2 ), 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |
| Chicago | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi. "Some Algebraic structures of Neutrosophic fuzzy sets." Journal of International Journal of Neutrosophic Science, 19 no. 2 (2022): 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |
| Harvard | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi. (2022). Some Algebraic structures of Neutrosophic fuzzy sets. Journal of International Journal of Neutrosophic Science, 19 ( 2 ), 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |
| Vancouver | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi. Some Algebraic structures of Neutrosophic fuzzy sets. Journal of International Journal of Neutrosophic Science, (2022); 19 ( 2 ): 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |
| IEEE | I. Silambarasan, R. Udhayakumar, Florentin Smarandache, Said Broumi, Some Algebraic structures of Neutrosophic fuzzy sets, Journal of International Journal of Neutrosophic Science, Vol. 19 , No. 2 , (2022) : 30-41 (Doi : https://doi.org/10.54216/IJNS.190203) |