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The additive consistency measure of fuzzy reciprocal preference relations

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Abstract

Fuzzy reciprocal preference relations (FPR) are one of the most common preference relations which decision makers (DMs) express their comparison information in decision making, and the consistency of preference relations is an important step for reasonable and reliable decision making. Based on the concept of deviation between two matrices, we develop some consistency measures for FPRs to ensure that the DMs are being neither random nor illogical. A consistency index \((CI)\) and the threshold \((\overline{CI})\) of FPRs are defined to measure whether a FPR is of acceptable consistency. For FPRs with unacceptable consistency, an optimization method and two iterative algorithms are presented to improve its consistency and the process terminates until the \(CI\) is controlled within the threshold \(\overline{CI}.\) Furthermore, one of algorithms is extended to handle group decision making (GDM) of FPRs. Finally, two examples and comparative analysis are furnished to demonstrate the effectiveness of the developed methods.

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Acknowledgements

The authors are very grateful to Associate Editor and the anonymous reviewers for their constructive comments and suggestions that have helped to improve the quality of this paper. This work was partly supported by the National Natural Science Foundation of China (NSFC) (No.71471056), the Key Project of National Natural Science Foundation of China (No.71433003), the Fundamental Research Funds for the Central Universities (No. 2015B23014), Excellent Innovative Talent Program of Hohai University, sponsored by Qing Lan Project of Jiangsu Province, and National “Twelfth Five-Year” Plan for Science & Technology Support (2015BAB07B01).

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Authors and Affiliations

  1. Business School, Hohai University, Nanjing, 211100, People’s Republic of China

    Yejun Xu, Xia Liu & Huimin Wang

  2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, People’s Republic of China

    Huimin Wang

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  1. Yejun Xu
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  2. Xia Liu
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  3. Huimin Wang
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Correspondence to Yejun Xu.

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Xu, Y., Liu, X. & Wang, H. The additive consistency measure of fuzzy reciprocal preference relations. Int. J. Mach. Learn. & Cyber. 9, 1141–1152 (2018). https://doi.org/10.1007/s13042-017-0637-0

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  • DOI: https://doi.org/10.1007/s13042-017-0637-0

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