Research Article

Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties

Volume: 7 Number: 2 October 15, 2019
EN

Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties

Abstract

In this paper, we combine the important concepts which are Fuzzy numbers and Fibonacci, Lucas numbers. We introduce the concepts of Fuzzy Fibonacci and Fuzzy Lucas numbers by this combination. By this motivation, we provide a bridge between the areas Fuzzy sets and number theory. Afterwards, we generalize their well-known properties by the definitions of Fuzzy Fibonacci and Lucas numbers.

Keywords

Fuzzy numbers,Fuzzy Fibonacci numbers,Fuzzy Lucas numbers

References

  1. \bibitem{Bandemer} Bandemer, H., Mathematics of Uncertainty: Ideas, Methods, Application Problems. Springer, New York, 2006. \bibitem{prade} Dubois, D. and Prade, H., Operations on Fuzzy Numbers,{\it Int. J. Systems Sci.,} 9-6, 613-626, 1978.
  2. \bibitem{Dubois} Dubois D. and Prade H., Towards fuzzy differential calculus. {\it Fuzzy Sets Syst.} 8 (1982) 1–17(I), 105–116(II), 225–234(III).
  3. \bibitem{Diamond} Diamond P. and Kloeden. P., Metric Spaces of Fuzzy Sets. World Scientific, Singapore, 1994.
  4. \bibitem{Dubois2} Dubois D. and Prade H., Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
  5. \bibitem{Dubois3} Dubois D. and Prade H., Ranking fuzzy numbers in a setting of possibility theory. {\it Inf. Sci.} 30 (1983) 183–224.
  6. \bibitem{Dubois4} Dubois D. and Prade H., Possibility Theory. An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, 1988.
  7. \bibitem{dubois5} Dubois D. and Prade H., (eds). Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series. Kluwer, Boston, 2000.
  8. \bibitem{dubois6} Dubois D., Kerre E., Mesiar R. and Prade H., Fuzzy interval analysis. In: D. Dubois and H. Prade (eds), Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series. Kluwer, Boston, 2000, pp. 483–581.
  9. \bibitem{gao} Gao, S., Zhang, Z. and Cao, C., Multiplication Operation on Fuzzy Numbers,{\it Journal of Software,} 4-4, 331-338, 2009.
  10. \bibitem{Goetschel} Goetschel R. and Voxman W., Elementary fuzzy calculus. {\it Fuzzy Sets Syst.} 18 (1986) 31–43.
APA
Irmak, N., & Demirtaş, N. (2019). Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties. Mathematical Sciences and Applications E-Notes, 7(2), 218-224. https://doi.org/10.36753/mathenot.634513
AMA
1.Irmak N, Demirtaş N. Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties. Math. Sci. Appl. E-Notes. 2019;7(2):218-224. doi:10.36753/mathenot.634513
Chicago
Irmak, Nurettin, and Naime Demirtaş. 2019. “Fuzzy Fibonacci and Fuzzy Lucas Numbers With Their Properties”. Mathematical Sciences and Applications E-Notes 7 (2): 218-24. https://doi.org/10.36753/mathenot.634513.
EndNote
Irmak N, Demirtaş N (October 1, 2019) Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties. Mathematical Sciences and Applications E-Notes 7 2 218–224.
IEEE
[1]N. Irmak and N. Demirtaş, “Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties”, Math. Sci. Appl. E-Notes, vol. 7, no. 2, pp. 218–224, Oct. 2019, doi: 10.36753/mathenot.634513.
ISNAD
Irmak, Nurettin - Demirtaş, Naime. “Fuzzy Fibonacci and Fuzzy Lucas Numbers With Their Properties”. Mathematical Sciences and Applications E-Notes 7/2 (October 1, 2019): 218-224. https://doi.org/10.36753/mathenot.634513.
JAMA
1.Irmak N, Demirtaş N. Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties. Math. Sci. Appl. E-Notes. 2019;7:218–224.
MLA
Irmak, Nurettin, and Naime Demirtaş. “Fuzzy Fibonacci and Fuzzy Lucas Numbers With Their Properties”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 2, Oct. 2019, pp. 218-24, doi:10.36753/mathenot.634513.
Vancouver
1.Nurettin Irmak, Naime Demirtaş. Fuzzy Fibonacci and Fuzzy Lucas Numbers with their Properties. Math. Sci. Appl. E-Notes. 2019 Oct. 1;7(2):218-24. doi:10.36753/mathenot.634513