On Bipolar-Valued Hesitant Fuzzy Sets and Their Applications in Multi-Attribute Decision Making
Abstract
In this manuscript, a novel structure of bipolar-valued hesitant fuzzy set (BPVHFS) is proposed as ageneralization of fuzzy set (FS). The basic set theoretic operations of BPVHFSs are defined and their
related results are studied. Based on the basic operations, some aggregation operators for BPVHFSs
are developed and their fitness is verified using principle of mathematical induction. The multiattribute
decision making (MADM) is established in the framework of BPVHFSs and a numerical
example is provided to illustrate the process. The article ended with some concluding remarks along
with some future directions.
References
L. Zadeh, “Fuzzy setsâ€, Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
K.M. Lee, “Bipolar-Valued Fuzzy sets and their operationsâ€, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, pp. 307-312, 2000.
N. Chen, Z.S. Xu and M. Xia, “Interval-valued hesitant preference relations and their applications to group decision makingâ€, Knowledge-Based Systems, vol. 37, pp. 528–540, 2013.
K. Atanassov, “Intuitionistic fuzzy setsâ€, Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986.
D.S.N. Ruiand L. Pierre, “Bipolarity in human reasoning and effective decision makingâ€, international journal of Intelligent Systems, vol. 23, pp. 898-922, 2008.
T. Mahmood and M. Munir, “On bipolar-valued fuzzy subgroupsâ€, World Applied Sciences Journal, vol. 27, no. 12, pp. 1806-1811, 2013.
M. Aslam, S. Abdullah and K. Ullah, “Bipolar fuzzy soft sets and its application in decision making problemâ€, Journal of Intelligent and fuzzy system, vol. 27, no. 2, pp. 729-742, 2014.
V. Torra and Y. Narukawa, “On hesitant fuzzy sets and decisionâ€, In 18th IEEE International Conference on Fuzzy Systems, Jeju Island Korea, IEEE, pp. 1378–1382, 2009.
V. Torra, “Hesitant fuzzy setsâ€, International Journal of Intelligent Systems, vol. 25, no 6, pp. 529–539, 2010.
N. Chen, Z. S. Xu, and M.M. Xia, “Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysisâ€. Applied Mathematical Modelling. Vol. 37, no 4, pp. 2197–2211, 2013.
M.M. Xia, Z.S. Xu and N. Chen, “Some hesitant fuzzy aggregation operators with their application in group decision makingâ€, Group Decision and Negotiation, vol. 22, no. 2, pp. 259–279, 2013.
D. Li, “Multi-attribute decision making models and methods using intuitionistic fuzzy setsâ€, Journal of Computer and System Sciences, vol. 70, no. 1, pp. 73-85, 2005.
M. Xia and Z.S. Xu, “Hesitant fuzzy information aggregation in decision makingâ€, International journal of approximate reasoning, vol. 52, no. 3, pp. 395-407, 2011.
Z.S. Xu and R.R. Yager, “Some geometric aggregation operators based on intuitionistic fuzzy setsâ€, International Journal of General Systems, vol. 35, no. 4, pp. 417–433, 2006.
Z.S. Xu, “Intuitionistic fuzzy aggregation operatorsâ€, IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1179-1187, 2007.
P. Zheng, “A note on operations of hesitant fuzzy setsâ€, International Journal of Computational Intelligence Systems, vol. 8, no. 2, pp. 226-239, 2015. [17] T. Mahmood, K. Ullah, Q. Khan and F. Smarandache, “Some aggregation operators for bipolar-valued hesitant fuzzy informationâ€, Journal of Fundamental and Applied Sciences, vol.10, no. 4S, pp. 240-245, 2018. [18] T. Mahmood, K. Ullah, N. Jan, I. Deli and Q. Khan, “Some aggregation operators for bipolar-valued hesitant fuzzy information based on Einstein operational lawsâ€, J. Engg. Appl. Sci., vol.36, no. 2, pp. 63-72, 2017. [19] T. Mahmood, P. Liu, J. Ye and Q. Khan, “Several hybrid aggregation operators for triangular intuitionistic fuzzy set and their application in multi-criteria decision makingâ€, Granular Computing, vol. 3, no. 2, pp. 153-168, 2018. [20] P. Liu, Q. Khan, J. Ye and T. Mahmood, “Group decision-making method under hesitant interval neutrosophic uncertain linguistic environmentâ€, Int. J. Fuzzy Systems, pp. 1-17, 2017, https://doi.org/10.1007/s40815-017-0445-4. [21] P. Liu, T. Mahmood and Q. Khan, “Multi-attribute decision-making based on prioritized aggregation operator under hesitant intuitionistic fuzzy linguistic environmentâ€, Symmetry, vol. 9, no. 11, 2017. [22] K. Ullah, T. Mahmood, and N. Jan, “Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognitionâ€, Symmetry, vol. 10, no. 6, 2018. [23] T. Mahmood, K. Ullah, Q. Khan and N. Jan, “An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets", Neural Computing and Applications, 2018, https://doi.org/10.1007/s00521-018-3521-2.