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Ordered weighted distance measure

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Abstract

The aim of this paper is to develop an ordered weighted distance (OWD) measure, which is the generalization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the min distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the min operator are also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve (or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low (or high) weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.

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Authors and Affiliations

  1. School of Economics and Management, Southeast University, Nanjing, Jiangsu, 210096, China

    Zeshui Xu

  2. School of Economics and Management, Tsinghua University, Beijing, 100084, China

    Jian Chen

Authors
  1. Zeshui Xu
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  2. Jian Chen
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Corresponding author

Correspondence to Zeshui Xu.

Additional information

The work was supported by the National Natural Science Foundation of China (No.70571087 and No.70321001), and the National Science Fund for Distinguished Young Scholars of China (No.70625005).

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, Nanjing, China. He is a Professor with Sciences Institute, PLA University of Science and Technology, Nanjing, China. He serves on the Editorial Boards of Information: An International Journal, International Journal of Applied Management Science, International Journal of Data Analysis Techniques and Strategies, Systems Engineering — Theory & Practice, and Fuzzy Systems and Mathematics. He has authored a book entitled Uncertain Multiple Attribute Decision Making: Methods and Applications (Tsinghua University Press, Beijing, 2004) and has contributed more than 180 journal articles to professional journals. His current research interests include information fusion, group decision making, computing with words, and aggregation operators.

Jian Chen received the B.Sc. degree in Electrical Engineering from Tsinghua University, Beijing, China, in 1983, and the M.Sc. and the Ph.D. degree both in Systems Engineering from the same University in 1986 and 1989, respectively. He is EMC Professor and Chairman of Management Science Department, Director of Research Center for Contemporary Management, Tsinghua University. His main research interests include supply chain management, E-commerce, decision support systems, modeling and control of complex systems. Dr. Chen has published over 100 papers in refereed journals and has been a principal investigator for over 30 grants or research contracts with National Science Foundation of China, governmental organizations and companies. He has been invited to present several plenary lectures. He is the recipient of Ministry of Education Changjiang Scholars, Fudan Management Excellence Award(3rd), Science and Technology Progress Awards of Beijing Municipal Government; the Outstanding Contribution Award of IEEE Systems, Man and Cybernetics Society; Science and Technology Progress Award of the State Educational Commission; Science & Technology Award for Chinese Youth. He has also been elected to IEEE Fellow. He serves as Chairman of the Service Systems and Organizations Technical Committee of IEEE Systems, Man and Cybernetics Society, Vice President of Systems Engineering Society of China, Vice President of China Society for Optimization and Overall Planning, a member of the Standing Committee of China Information Industry Association. He is the editor of “the Journal of Systems Science and Systems Engineering”, an area editor of “Electronic Commerce Research and Applications”, an associate editor of “IEEE Transactions on Systems, Man and Cybernetics: Part A”, “IEEE Transactions on Systems, Man and Cybernetics: Part C”, and “Asia Pacific Journal of Operational Research” and serves on the Editorial Board of “International Journal of Electronic Business”, “International Journal of Information Technology and Decision Making” and “Systems Research and Behavioral Science”.

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Xu, Z., Chen, J. Ordered weighted distance measure. J. Syst. Sci. Syst. Eng. 17, 432–445 (2008). https://doi.org/10.1007/s11518-008-5084-8

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  • DOI: https://doi.org/10.1007/s11518-008-5084-8

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