Abstract
We first propose a series of similarity measures for intuitionistic fuzzy values (IFVs) based on the intuitionistic fuzzy operators (Atanassov 1995). The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.
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The work was supported in part by the National Science Fund for Distinguished Young Scholars of China (No.70625005), the National Natural Science Foundation of China (No.71071161), and the Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province (No.CX10B_059Z).
Meimei Xia received the B.E. degree in information management and information system from College of Operations Research and Management, Qufu Normal University, Rizhao, China, in 2009. She is currently working toward the Ph.D. degree at School of Economics and Management, Southeast University. Her research interests include aggregation operators and group decisoin making.
Zeshui Xu received the Ph.D. degree in management science and engineering from Southeast University, Nanjing, China, in 2003. From April 2003 to May 2005, he was a Postdoctoral Researcher with the School of Economics and Management, Southeast University. From October 2005 to December 2007, he was a Postdoctoral Researcher with the School of Economics and Management, Tsinghua University, Beijing, China. He is an Adjunct Professor with the School of Economics and Management, Southeast University. He is a Chair Professor with the Institute of Sciences, PLA University of Science and Technology, Nanjing. He is a member of the Editorial Boards of Information: An International Journal, the International Journal of Applied Management Science, the International Journal of Data Analysis Techniques and Strategies, and the System Engineering — Theory and Practice and Fuzzy Systems and Mathematics. He has authored three books and contributed more than 250 journal articles to professional journals. His current research interests include information fusion, group decision making, computing with words, and aggregation operators.
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Xia, M., Xu, Z. Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J. Syst. Sci. Syst. Eng. 19, 430–452 (2010). https://doi.org/10.1007/s11518-010-5151-9
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DOI: https://doi.org/10.1007/s11518-010-5151-9