Fuzzy Multi-Criteria Decision Making Algorithm under Intuitionistic Hesitant Fuzzy Set with Novel Distance Measure
Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Sivasagar- 785697, India.
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, India.
Department of Mathematics, Dibrugarh University, Dibrugarh-786004, India.
Received on August 15, 2019
Accepted on January 19, 2020
Decision making under uncertainty is a crucial issue and most demanding area of research now a days. Intuitionistic hesitant fuzzy set plays important role in dealing with the circumstances in which decision makers judge an alternative with a collection membership grades and a collection of non-membership grades. This paper contributes a novel and advanced distance measure between Intuitionistic Hesitant fuzzy sets (IHFSs). A comparative analysis of the present distance measure with existing measures is performed first. Afterwards, a case study is carried in multi-criteria decision making problem to exhibit the applicability and rationality of the proposed distance measure. The advantage of the proposed distance measure over the existing distance measures is that in case of deficit number of elements in IHFs, a decision maker can evaluate distance measure without adding extra elements to make them equivalent and furthermore, it works in successfully in all the situations.
Keywords- Hesitant fuzzy set, Intuitionistic fuzzy set, Intuitionistic hesitant fuzzy set, Fuzzy multi criteria decision making.
Saikia, R., Garg, H., & Dutta, P. (2020). Fuzzy Multi-Criteria Decision Making Algorithm under Intuitionistic Hesitant Fuzzy Set with Novel Distance Measure. International Journal of Mathematical, Engineering and Management Sciences, 5(3), 473-487. https://doi.org/10.33889/IJMEMS.2020.5.3.039.
Conflict of Interest
The authors confirm that there is no conflict of interest to declare for this publication.
The authors would like to express their sincere thanks to the editor and anonymous reviews for their time and valuable suggestions.
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.
Beg, I., & Rashid, T. (2014a). Group decision making using intuitionistic hesitant fuzzy sets. International Journal of Fuzzy Logic and Intelligent Systems, 14(3), 181-187.
Beg, I., & Rashid, T. (2014b). Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS. Opsearch, 51(1), 98-129.
Bellman, R.E., & Zadeh, L.A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B141-B164.
Chen, J., & Huang, X. (2017). Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making. Journal of Nonlinear Sciences and Applications, 10(3), 1012-1029.
Chen, X., Li, J., Qian, L., & Hu, X. (2016, January). Distance and similarity measures for intuitionistic hesitant fuzzy sets. In 2016 International Conference on Artificial Intelligence: Technologies and Applications. doi:10.2991/icaita-16.2016.46.
Deepak, D., Mathew, B., John, S.J., & Garg, H. (2019). A topological structure involving hesitant fuzzy sets. Journal of Intelligent & Fuzzy Systems, 36(6), 6401-6412.
Faizi, S., Rashid, T., Xu, Z., & Zafar, S. (2018). Distance measures for hesitant intuitionistic fuzzy linguistic term sets based on a risk factor parameter. International Journal of Computers and Applications, 41(6), 418-435.
Garg, H., & Arora, R. (2017). Distance and similarity measures for dual hesitant fuzzy soft sets and their applications in multicriteria decision making problem. International Journal for Uncertainty Quantification, 7(3), 229-248.
Garg, H., & Kaur, G. (2018a). Novel distance measures for cubic intuitionistic fuzzy sets and their applications to pattern recognitions and medical diagnosis. Granular Computing, 1-16. Doi: 10.1007/s41066-018-0140-3.
Garg, H., & Kaur, G. (2018b). Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision-making based on aggregation operators with new distance measures. Mathematics, 6(12), 280.
Garg, H., & Kaur, G. (2020). Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Computers & Industrial Engineering, 140, 106211.
Garg, H., & Kumar, K. (2020). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artificial Intelligence Review, 53, 595-624.
Garg, H., & Kumar, K. (2018). Distance measures for connection number sets based on set pair analysis and its applications to decision-making process. Applied Intelligence, 48(10), 3346-3359.
Li, X., & Chen, X. (2018). D-intuitionistic hesitant fuzzy sets and their application in multiple attribute decision making. Cognitive Computation, 10(3), 496-505.
Liu, X., Ju, Y., & Yang, S. (2014). Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 27(3), 1187-1201.
Nazra, A., Syafruddin, Lestari, R., & Wicaksono, G.C. (2017, September). Hesitant intuitionistic fuzzy soft sets. In Journal of Physics: Conference Series, 890(1), 012118. IOP Publishing.
Peng, J.J., Wang, J.Q., Wang, J., & Chen, X.H. (2014). Multicriteria decision-making approach with hesitant interval-valued intuitionistic fuzzy sets. The Scientific World Journal, 2014. Article ID 868515.
Rani, D., & Garg, H. (2017). Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. International Journal for Uncertainty Quantification, 7(5), 423-439.
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529-539.
Xia, M., Xu, Z., & Chen, N. (2013). Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decision and Negotiation, 22(2), 259-279.
Xu, Z.S., & Yager, R.R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417-433.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
Zhou, W., Xu, Z., & Chen, M. (2015). Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Computers & Industrial Engineering, 87, 163-175.