Abstract
This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation (IFPR). An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR. By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR, a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency. An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity. The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible. Numerical examples are presented to illustrate how to apply the proposed approaches.
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Wu-Yong Qian holds his educational degrees (B.Sc., M.Sc., and Ph.D.) in mathematics, and Management Science and Engineering from Jiangsu Normal University, and Nanjing University of Aeronautics and Astronautics. Currently, he is currently with the School of Business at Jiangnan University. He has published 16 research papers. He has been working in the areas of the grey systems theory and decision analysis.
Kevin W. Li received his B.Sc. in control sciences and M.A.Sc. in systems engineering from Xiamen University, Xiamen, China, in 1991 and 1994, respectively, and Ph.D. in systems design engineering from the University of Waterloo, Waterloo, Canada in 2003. Dr. Li is a Professor in the Odette School of Business at the University of Windsor, Windsor, Canada. His research interests are concerned with finding equitable and sustainable solutions to complex decision problems. His papers have appeared in reputable journals such as Computers and Operations Research, European Journal of Operational Research, IEEE Transactions on Fuzzy Systems, IEEE Transactions on Systems, Man, and Cybernetics, Information Sciences, International Journal of Production Economics, and Journal of the Operational Research Society. In 2011, Dr. Li was awarded a Japan Society for the Promotion of Science (JSPS) Invitation Fellowship. His research has been supported by two Natural Sciences and Engineering Research Council of Canada Discovery Grants.
Zhou-Jing Wang received his B.Sc. degree in control theory from Xiamen University, Xiamen, China, in 1985, M.A.Sc. in computer sciences from the National University of Defense Technology in Changsha, China, in 1988, and Ph.D. in computer sciences from Beihang University, Beijing, China, in 2012. He is currently a Professor in the School of Information at Zhejiang University of Finance & Economics, Hangzhou, China. His research interests include preference modeling and decision analysis. Professor Wang has published his research in highly respected refereed journals such as European Journal of Operational Research, Information Sciences, Expert Systems with Applications, Computers & Industrial Engineering and Applied Mathematical Modelling. His research projects have received financial support from the National Natural Science Foundation of China.
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Qian, WY., Li, K.W. & Wang, ZJ. Approaches to improving consistency of interval fuzzy preference relations. J. Syst. Sci. Syst. Eng. 23, 460–479 (2014). https://doi.org/10.1007/s11518-014-5259-4
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DOI: https://doi.org/10.1007/s11518-014-5259-4