Ranking Method for Z-numbers based on Centroid-Point

Authors

  • Mujahid Abdullahi Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Sule Lamido University, Kafin Hausa 048, Jigawa State
  • Tahir Ahmad Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.
  • Abdulhakeem Olayiwola, Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Sule Lamido University 048 SLU Kafin Hausa, Jigawa, Nigeria.
  • Salisu Garba Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Sule Lamido University 048 SLU Kafin Hausa, Jigawa, Nigeria.
  • Auwal Mustapha Imam Physics with Electronics Department, Federal University Birnin Kebbi, 862104, Kebbi State, Nigeria
  • Babangida Isyaku Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Sule Lamido University 048 SLU Kafin Hausa, Jigawa, Nigeria.

DOI:

https://doi.org/10.56471/slujst.v2i1.76

Abstract

Context: Zadeh introduced the concept of Z-number to provide a basis for computation with numbers that are not completely reliable, and it has the ability to portray fuzziness and reliability of information concurrently. Ranking of Z-numbers is an important aspect, especially in decision making Objective: Ranking method for Z-numbers. Method: By converting Z-number into fuzzy number, and then the centroid-point method and decision rules are used to rank the obtained fuzzy numbers. Results: A ranking method for Z-numbers is proposed, and a numerical example is provided to illustrate the feasibility and validity of the proposed method. Conclusions: However, converting Z-number into fuzzy number can lead to loss of original Z-information.

References

Abdullah, L., & Jamal, N. J. (2010). Centroid-point of ranking fuzzy numbers and its application to health-related quality of life indicators. International Journal on Computer Science and Engineering, 2(08), 2773-2777.

Abdullahi, M., Ahmad, T., & Ramachandran, V. (2020). A Review on Some Arithmetic Concepts of Z-Number and its Application to Real-World Problems. International Journal of Information Technology & Decision Making.

Aliev, R. A., Huseynov, O. H., & Serdaroglu, R. (2016a). Ranking of Z-numbers and its application in decision making. International Journal of Information Technology & Decision Making, 15(06), 1503-1519.

Aliev, R. A., Alizadeh, A. V., & Huseynov, O. H. (2015a). The arithmetic of discrete Z-numbers. Information Sciences, 290, 134-155.

Aliev, R. A., Huseynov, O. H., Aliyev, R. R., & Alizadeh, A. A. (2015b). The arithmetic of Z-numbers: Theory and applications. Singapore: World Scientific.

Aliev, R. A., Huseynov, O. H., & Zeinalova, L. M. (2016b). The arithmetic of continuous Z-numbers. Information Sciences, 373, 441-460.

Bakar, A. S. A., & Gegov, A. (2015). Multi-layer decision methodology for ranking Z-numbers. International Journal of Computational Intelligence Systems, 8(2), 395-406.

Ezadi, S., & Allahviranloo, T. (2017). New multi-layer method for Z-number ranking using hyperbolic tangent function and convex combination. Intelligent Automation & Soft Computing, 1-7.

Gong, Y., Li, X., & Jiang, W. (2020, August). A New Method for Ranking Discrete Z-number. In 2020 Chinese Control And Decision Conference (CCDC) (pp. 3591-3596). IEEE.

Glukhoded, E. A., & Smetanin, S. I. (2016). The method of converting an expert opinion to Z-number. Proceedings of the Institute for System Programming PAS, 28(3).

Jiang, W., Xie, C., Luo, Y., & Tang, Y. (2017). Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 32(3), 1931-1943.

Kang, B., Wei, D., Li, Y., & Deng, Y. (2012). A method of converting Z-number to classical fuzzy number. Journal of Information &Computational Science, 9(3), 703-709.

Mohamad, D., Shaharani, S. A., & Kamis, N. H. (2017, August). Ordering of Z-numbers. In AIP Conference Proceedings (Vol. 1870, No. 1, p. 040049). AIP Publishing LLC.

Qiu, D., Xing, Y., & Dong, R. (2018). On Ranking of Continuous Z‐Numbers with Generalized Centroids and Optimization Problems Based on Z‐Numbers. International Journal of Intelligent Systems, 33(1), 3-14.

Wang, Y. M., Yang, J. B., Xu, D. L., & Chin, K. S. (2006). On the centroids of fuzzy numbers. Fuzzy sets and systems, 157(7), 919-926.

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

Zadeh, L. A. (2011a). A note on Z-numbers. Information Sciences, 181(14), 2923-2932.

Zadeh, L. A. (2011b). The concept of a Z-number-A new direction in uncertain computation. In 2011 IEEE International Conference on Information Reuse & Integration (pp. xxii-xxiii). IEEE.

Published

2021-01-23