International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 19 , Issue 2 , PP: 30-41, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Some Algebraic structures of Neutrosophic fuzzy sets

I. Silambarasan 1 * , R. Udhayakumar 2 , Florentin Smarandache 3 , Said Broumi 4

  • 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)
  • Doi: https://doi.org/10.54216/IJNS.190203

    Received: March 08, 2022 Accepted: September 03, 2022
    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.

    Cite This Article As :
    Silambarasan, I.. , Udhayakumar, R.. , Smarandache, Florentin. , Broumi, Said. Some Algebraic structures of Neutrosophic fuzzy sets. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 30-41. DOI: https://doi.org/10.54216/IJNS.190203
    Silambarasan, I. Udhayakumar, R. Smarandache, F. Broumi, S. (2022). Some Algebraic structures of Neutrosophic fuzzy sets. International Journal of Neutrosophic Science, (), 30-41. DOI: https://doi.org/10.54216/IJNS.190203
    Silambarasan, I.. Udhayakumar, R.. Smarandache, Florentin. Broumi, Said. Some Algebraic structures of Neutrosophic fuzzy sets. International Journal of Neutrosophic Science , no. (2022): 30-41. DOI: https://doi.org/10.54216/IJNS.190203
    Silambarasan, I. , Udhayakumar, R. , Smarandache, F. , Broumi, S. (2022) . Some Algebraic structures of Neutrosophic fuzzy sets. International Journal of Neutrosophic Science , () , 30-41 . DOI: https://doi.org/10.54216/IJNS.190203
    Silambarasan I. , Udhayakumar R. , Smarandache F. , Broumi S. [2022]. Some Algebraic structures of Neutrosophic fuzzy sets. International Journal of Neutrosophic Science. (): 30-41. DOI: https://doi.org/10.54216/IJNS.190203
    Silambarasan, I. Udhayakumar, R. Smarandache, F. Broumi, S. "Some Algebraic structures of Neutrosophic fuzzy sets," International Journal of Neutrosophic Science, vol. , no. , pp. 30-41, 2022. DOI: https://doi.org/10.54216/IJNS.190203