Document Type : Research Paper
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang, Bandar Tun Abdul Razak Jengka, Pahang, Malaysia.
Centre for Mathematical Sciences, Universiti Malaysia Pahang, Gambang, Malaysia.
Mathematics Division, Centre for Foundation Studies in Science, University of Malaya, Kuala Lumpur, Malaysia.
Management Science Research Group, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus, 21030 Kuala Terengganu, Terengganu, Malaysia.
In fuzzy decision-making, incomplete information always leads to uncertain and partially reliable judgements. The emergence of fuzzy set theory helps decision-makers in handling uncertainty and vagueness when making judgements. Intuitionistic Fuzzy Numbers (IFN) measure the degree of uncertainty better than classical fuzzy numbers, while Z-numbers help to highlight the reliability of the judgements. Combining these two fuzzy numbers produces Intuitionistic Z-Numbers (IZN). Both restriction and reliability components are characterized by the membership and non-membership functions, exhibiting a degree of uncertainties that arise due to the lack of information when decision-makers are making preferences. Decision information in the form of IZN needs to be defuzzified during the decision-making process before the final preferences can be determined. This paper proposes an Intuitive Multiple Centroid (IMC) defuzzification of IZN. A novel Multi-Criteria Decision-Making (MCDM) model based on IZN is developed. The proposed MCDM model is implemented in a supplier selection problem for an automobile manufacturing company. An arithmetic averaging operator is used to aggregate the preferences of all decision-makers, and a ranking function based on centroid is used to rank the alternatives. The IZN play the role of representing the uncertainty of decision-makers, which finally determine the ranking of alternatives.
- Aliev, R. A. (2013). Uncertain preferences and imperfect information in decision making. In fundamentals of the fuzzy logic-based generalized theory of decisions(pp. 89-125). Springer, Berlin, Heidelberg.
- Aliev, R. A., Guirimov, B. G., Huseynov, O. H., & Aliyev, R. R. (2021). A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iranian journal of fuzzy systems, 18(4), 37-49.
- Sirbiladze, G. (2021). New view of fuzzy aggregations. part I: general information structure for decision-making models. Journal of fuzzy extension and applications, 2(2), 130-143.
- Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
- Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141. https://doi.org/10.1287/mnsc.17.4.B141
- Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3), 199-249.
- Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-III. Information sciences, 9(1), 43-80.
- Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International journal of systems science, 9(6), 613-626.
- Chen, S. J., & Hwang, C. L. (1992). Fuzzy multiple attribute decision making methods. In fuzzy multiple attribute decision making(pp. 289-486). Springer, Berlin, Heidelberg.
- Chang, D. Y. (1996). Applications of the extent analysis method on fuzzy AHP. European journal of operational research, 95(3), 649-655.
- Bhattacharya, J. (2021). Some results on certain properties of intuitionistic fuzzy sets. Journal of fuzzy extension and applications, 2(4), 377-387.
- Atanassov, K. T. (1986). Intuitionistic fuzzy set. Fuzzy sets and systems, 20, 87–97.
- Xue, Y., & Deng, Y. (2021). Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. Applied intelligence, 51(8), 6224-6233.
- Husain, S., Ahmad, Y., & Alam, M. A. (2012). A study on the role of intuitionistic fuzzy set in decision making problems. International journal of computer applications, 48(0975-888), 35-41.
- Rahman, A. U., Ahmad, M. R., Saeed, M., Ahsan, M., Arshad, M., & Ihsan, M. (2020). A study on fundamentals of refined intuitionistic fuzzy set with some properties. Journal of fuzzy extension and applications, 1(4), 279-292.
- Gautam, S. S., & Singh, S. R. (2016). TOPSIS for multi criteria decision making in intuitionistic fuzzy environment. International journal of computer applications, 156(8), 42-49.
- Wang, C. H., & Wang, J. Q. (2016). A multi-criteria decision-making method based on triangular intuitionistic fuzzy preference information. Intelligent automation & soft computing, 22(3), 473-482.
- Kaur, P. (2014). Selection of vendor based on intuitionistic fuzzy analytical hierarchy process. Advances in operations research, 2014.
- 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 &computational science, 9(3), 703-709.
- Kang, B., Wei, D., Li, Y., & Deng, Y. (2012). Decision making using Z-numbers under uncertain environment. Journal of computational information systems, 8(7), 2807-2814.
- Ku Khalif, K. M. N., Gegov, A., & Abu Bakar, A. S. (2017). Hybrid fuzzy MCDM model for Z-numbers using intuitive vectorial centroid. Journal of intelligent & fuzzy systems, 33(2), 791-805.
- Sari, I. U., & Kahraman, C. (2020, July). Intuitionistic fuzzy Z-numbers. International conference on intelligent and fuzzy systems(pp. 1316-1324). Istanbul, Turkey. Springer, Cham. https://link.springer.com/chapter/10.1007/978-3-030-51156-2_154
- Arun Prakash, K., Suresh, M., & Vengataasalam, S. (2016). A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept. Mathematical sciences, 10(4), 177-184.
- Wang, F., & Mao, J. (2019). Approach to multicriteria group decision making with Z-numbers based on TOPSIS and power aggregation operators. Mathematical problems in engineering, 2019.