Ordered discrete and continuous Z-numbers
DOI:
https://doi.org/10.11113/mjfas.v16n4.1632Keywords:
Z-number, Discrete Z-number, Continuous Z-number, Relation, LatticeAbstract
Both discrete and continuous Z-numbers are pairs of discrete and continuous fuzzy numbers. Even though the later are ordered, this do not simply imply the discrete and continuous Z-numbers are ordered as well. This paper proposed the idea of ordered discrete and continuous Z-numbers, which are necessary properties for constructing temporal Z-numbers. Linear ordering relation, , is applied between set of discrete or continuous Z-numbers and any arbitrary ordered subset of to obtain the properties.
References
Aliev, R. A., Alizadeh, A. V., Huseynov, O. H. 2017. An introduction to the arithmetic of Z-numbers by using horizontal membership functions. Procedia Computer Science, 120, 349-356.
Zadeh, L. A. 2011. A note on Z-numbers. Information Sciences, 181(14): 2923–2932.
Kang, B., Wei, D., Li, Y., Deng, Y. 2012. A method of converting Z-number to classical fuzzy number. Journal of Information and Computer Science, 9(3), 703–709.
Aliev, R. A., Alizadeh, A. V., Huseynov, O. H. 2015. The arithmetic of discrete Z-numbers. Information Sciences, 290, 134–155.
Aliev, R. A., Huseynov, O. H., Zeinalova L. M. 2016. The arithmetic of continuous Z-numbers. Information Sciences, 373: 441–460.
Aziz, A. R., Akif, A., Rafiq, A. R. 2015. The Arithmetic of Z-numbers: Theory and Applications. World Scientific.
Birkhoff G. 1940. Lattice Theory. American Mathematics Society.
Casasnovas, J., Riera, J. V. 2006. On the addition of discrete fuzzy numbers. Proceedings of the 5th WSEAS international conference on Telecommunications and informatics. World Scientific and Engineering Academy and Society (WSEAS), 432–437.
Alizadeh, A. V., Huseynov, O. Minimum and Maximum of discrete Z-numbers. 11th International Conference on Application of Fuzzy Systems and Soft Computing 2014. IEEE.
Kosanovic, B. R., Chaparro, L. F., Sclabassi, R. J. 1996, May. Signal modeling with dynamic fuzzy sets. International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings (Vol. 5, pp. 2829-2832). IEEE.
Abdullahi, M., Ahmad, T., Ramachandran, V. 2019. A radical approach for assessing EEG signal of an epileptic seizure using temporal discrete Z-numbers. 1st ICUW19 International Conference on Universal Wellbeing, 4-6 December 2019, Kuala Lumpur.
Aliev, R., Guirimov, B. 2018. Z-Number clustering based on general type-2 fuzzy sets. International Conference on Theory and Applications of Fuzzy Systems and Soft Computing. Springer.