Some New Identities for Fuzzy Fibonacci Number

Year 2023, Volume: 15 Issue: 2, 212 - 217, 31.12.2023

Merve Güney Duman

https://doi.org/10.47000/tjmcs.1167848

Abstract

With fuzzy logic, the concept of belonging to the sets has been replaced by the concept of how much they belong to the set. The subject of fuzzy sets was discussed and fuzzy logic studies have been done in many fields. Recently, the Fuzzy Fibonacci number sequence was defined using Fibonacci number sequences. In this study, we give some new properties related to fuzzy Fibonacci numbers.

Keywords

Fibonacci number, fuzzy number, fuzzy set, fuzzy Fibonacci number

References

• Abraham, A.M., Fuzzy Logic for Embedded System Application, Ph.D. senior member, IEEE, 2004.
• Bezdek, J., Keller, J., Krishnapuram, R., Pal, N. R., Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
• Buckley, J.J., Eslami, E., Introduction to Fuzzy Logic and Fuzzy Sets, Physica-Verlag, Heidelberg, Germany, 2002.
• Chalam, G.A., Fuzzy goal programming (FGP) approach to a stochastic transportation problem under budgetary constraint, Fuzzy Sets and Systems, 66(1994), 293–299.
• Dijkman, J.G., Van Haeringen, H., De Lange, S.T., Fuzzy numbers, J. Math. Anal. Appl., 92(1983), 301–341.
• Dubois, D., Prade, H., Operations on fuzzy numbers, International Journal of Systems Science, 6(9)(1978), 613–626.
• Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
• Dubois, D., Prade, H., Ranking fuzzy numbers in a setting of possibility theory, Inf. Sci., 30(1983), 183–224.
• Dubois, D., Prade, H., Possibility Theory, An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.
• Gao, S., Zhang, Z., Cao, C., Multiplication operation on fuzzy numbers, Journal of Software, 4(4)(2009), 331–338.
• Gegov, A., Fuzzy Networks for Complex Systems: A Modular Rule Base Approach, Springer, Berlin, 2010.
• Gegov, A, Sanders, D, Vatchova, B, Complexity management methodology for fuzzy systems with feedforward rule bases, Knowledge Based and Intelligent Engineering Systems, 19, 83–95.
• Hirota, K., Industrial Applications of Fuzzy Technology, Springer, Tokyo, 1993.
• Irmak, N., Demirtaş, N.,Fuzzy Fibonacci and fuzzy Lucas numbers with their properties, Mathematical Sciences and Applications E-Notes, 7(2)(2019), 218–224.
• Kecman, V., Learning and Soft Computing Support Vector Machines, Neural Networks, and Fuzzy Logic Models, A Bradford Book, the MIT Press, 2001.
• Klir, G. J., Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, N.J., 1995.
• Paksoy, P., Pehlivan, N.Y., Özceylan, E., Bulanık Ku¨me Teorisi, Nobel Yayınları, Ankara, 2013.
• Ribenboim, P., My Numbers, My Friends: Popular Lectures on Number Theory, Springer-Verlag New York, Inc., 2000.
• Roychowdhury, S., Pedrycz, W., A survey of defuzzification strategies, International Journal of Intelligent Systems, 16(6)(2001), 679–695.
• Sakawa, M., Yano, H.,An interactive fuzzy satisfying method using augmented minimax problems and its application to environmental systems, IEEE Trans. Syst. Man. Cybern, 15(1985), 720–729.
• Terano, T., Asai, K., Sugeno, M., Applied Fuzzy Systems, Academic Press Professional, Boston, 1994.
• Zimmermann, H.J., Fuzzy Sets, Decision Making, and Expert Systems, Vol. 10, Springer Science & Business Media, 1987.
• Zimmermann, H.J., Fuzzy Set Theory and Its Applications, Kluwer Academic Publishers, Boston, 1991.
• Zadeh, L.A. , Fuzzy sets, Information and Control, 8(3)(1965).