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A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

  • Liu, Fang
  • Zhang, Wei-Guo
  • Wang, Zhong-Xing
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    In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 3 ()
    Pages: 747-754

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:747-754
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Michele Fedrizzi & Silvio Giove, 2006. "Incomplete pairwise comparison and consistency optimization," Working Papers 144, Department of Applied Mathematics, Università Ca' Foscari Venezia.
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    7. S. Alonso & E. Herrera-Viedma & F. Chiclana & F. Herrera, 2009. "Individual And Social Strategies To Deal With Ignorance Situations In Multi-Person Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 313-333.
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