A Note on the Fuzzy Leonardo Numbers
Elen Viviani Pereira Spreafico
1
(
Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande, Brazil.
)
Eudes Antonio Costa
2
(
Department of Mathematics, Federal University of Tocantins, Arraias, Brazil.
)
Paula Maria Machado Cruz Catarino
3
(
Department of Mathematics, University of Trs-os-Montes e Alto Douro, Vila Real, Portugal.
)
کلید واژه: Triangular fuzzy numbers, Fuzzy Fibonacci numbers, Fuzzy Lucas numbers, Leonardo numbers, Algebraic properties, Identities, Sum identities.,
چکیده مقاله :
In this work, we define a new sequence denominated by fuzzy Leonardo numbers. Some algebraic properties of this new sequence are studied and several identities are established. Moreover, the relations between the fuzzy Fibonacci and fuzzy Lucas numbers are explored, and several results are given. In addition, some sums involving fuzzy Leonardo numbers are provided.
چکیده انگلیسی :
In this work, we define a new sequence denominated by fuzzy Leonardo numbers. Some algebraic properties of this new sequence are studied and several identities are established. Moreover, the relations between the fuzzy Fibonacci and fuzzy Lucas numbers are explored, and several results are given. In addition, some sums involving fuzzy Leonardo numbers are provided.
[1] Koshy T. Pell and Pell-Lucas numbers with applications. Springer, New York, 2014. https://link.springer.com/book/10.1007/978-1-4614-8489-9
[2] Koshy T. Fibonacci and Lucas Numbers with Applications, Springer, Volume 1, John Wiley and Sons, New Jersey, 2018.
[3] Koshy T. Fibonacci and Lucas Numbers with Applications, Springer, Volume 2, John Wiley and Sons, New Jersey, 2019.
[4] Catarino P, Borges A. On Leonardo numbers. Acta Mathematica Universitatis Comenianae. 2020; 89(1): 75-86. http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1005/799
[5] Alp Y, Ko¸cer EG. Some properties of Leonardo numbers. Konuralp Journal of Mathematics. 2021; 9(1): 183-189. https://dergipark.org.tr/en/download/article-file/1472020
[6] Alves, FRV, Vieira RPM. The Newton Fractals Leonardo Sequence Study with the Google Colab. International Electronic Journal of Mathematics Education. 2020; 15: 1-9. DOI: https://doi.org/10.29333/iejme/6440
[7] Catarino P, Borges A. A Note on Incomplete Leonardo Numbers. Integers. 2020; 20: #A43. https://math.colgate.edu/ integers/u43/u43.pdf
[8] Gokbas H. A New Family of Number Sequences: Leonardo-Alwyn Numbers. Armenian Journal of Mathematics. 2023; 15(6): 1-13. DOI: https://doi.org/10.52737/18291163-2023.15.6-1-13
[9] Kara N, Yilmaz F. On Hybrid Numbers with Gaussian Leonardo Coefficients. Mathematics. 2023, 11(6): 1-12. DOI: https://doi.org/10.3390/math11061551
[10] Kuhapatanakul K, Chobsorn J. On the Generalized Leonardo Numbers. Integers. 2022; 22: #A48. https://math.colgate.edu/ integers/w48/w48.pdf
[11] Tan E, Leung HH. On Leonardo p-numbers. Integers. 2023; 23: #A7. https://math.colgate.edu/ integers/x7/x7.pdf
[12] Mordeson JN, Mathew S. Families of Fuzzy Sets and Lattice Isomorphisms Preparation. Transactions on Fuzzy Sets and Systems. 2024; 3(2): 184-191. DOI: https://doi.org/10.30495/TFSS.2024.1119653
[13] Tomasiello S, Pedrycz W, Loia V. Fuzzy Numbers. In: Contemporary Fuzzy Logic. Big and Integrated Artificial Intelligence, Volume 1. Springer, Cham, 2022.
[14] Trillas E, Soto AR. On a New View of a Fuzzy Set. Transactions on Fuzzy Sets and Systems. 2023; 2(1): 92-100. DOI: https://doi.org/10.30495/tfss.2022.1971064.1051
[15] Zadeh LA. Fuzzy Sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[16] Dubois D, Prade H. Operations on fuzzy numbers. International Journal of Systems Science. 1978; 6(9): 613626. DOI: https://doi.org/10.1080/00207727808941724
[17] Dubois D, Prade H. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
[18] Dubois D., Prade H. Ranking fuzzy numbers in a setting of possibility theory. Information Sciences. 1983; 30: 183224. DOI: https://doi.org/10.1016/0020-0255(83)90025-7
[19] Dubois D, Prade, H. Possibility Theory, An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, 1988.
[20] Duman MG. Some New Identities for Fuzzy Fibonacci Number, Turkish Journal of Mathematics and Computer Science. 2023, 15(2): 212217. DOI: https://doi.org/10.47000/tjmcs.1167848
[21] Gao S, Zhang Z, Cao C. Multiplication Operation on Fuzzy Numbers. Journal of Software. 2009; 4(4): 331-338. DOI: https://doi.org/10.4304/jsw.4.4.331-338
[22] Roychowdhury S, Pedrycz W. A survey of defuzzyfication strategies. International Journal of Intelligent Systems. 2001; 16(6): 679695. DOI: https://doi.org/10.1002/int.1030
[23] Irmak N, Demirtas N. Fuzzy Fibonacci and fuzzy Lucas numbers with their properties, Mathematical Sciences and Applications E-Notes. 2019; 7(2): 218224. DOI: https://doi.org/10.36753/mathenot.634513
