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A goal programming approach to group decision-making with three formats of incomplete preference relations

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Abstract

This paper proposes a goal programming approach to solve the group decision-making problem where the preference information about alternatives provided by decision makers can be represented in three formats, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations and incomplete linguistic preference relations. In the approach, a transformation function is introduced to transform the incomplete linguistic preference relation into an incomplete fuzzy preference relation. To narrow the gap between the collective opinion and each decision maker’s opinion, a liner goal programming model is constructed to integrate the three different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. Thus, the ranking order of alternatives or selection of the most desirable alternative(s) is obtained directly according to the computed collective ranking values. A numerical example is also used to illustrate the feasibility and the applicability of the proposed approach.

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Acknowledgments

This research was partly supported by the National Science Funds for Distinguished Young Scientists of China (Project No. 70525002), the National Science Funds for Creative Research Groups of China (Project No. 70721001), National Science Foundation of China (NSFC, Project Nos. 70701008 and 90924016) and National Postdoctoral Foundation of China (Special Funding) (Project No. 200801394). The authors also wish to thank the editor and the anonymous reviewers for their helpful comments and suggestions on an earlier version of this manuscript.

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Authors and Affiliations

  1. Department of Management Science and Engineering, Northeastern University, Shenyang, China

    Zhi-Ping Fan

  2. Department of Economics, School of Business Administration, Northeastern University, 110004, Shenyang, China

    Yao Zhang

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  1. Zhi-Ping Fan
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  2. Yao Zhang
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Correspondence to Yao Zhang.

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Fan, ZP., Zhang, Y. A goal programming approach to group decision-making with three formats of incomplete preference relations. Soft Comput 14, 1083–1090 (2010). https://doi.org/10.1007/s00500-009-0503-4

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