The optimal group consensus deviation measure for multiplicative preference relations

  • Authors:

  • Zai-Wu Gong;Jeffrey Forrest;Yue Zhao;Ying-Jie Yang

  • Affiliations:

  • College of Economics and Management, Nanjing University of Information Science and Technology, Nanjing 210044, China and College of Applied Meteorology, Nanjing University of Information Science a ...;International Institute for General Systems Studies, 23 Kings Lane, Grove City, PA 16127, USA;College of Economics and Management, Nanjing University of Information Science and Technology, Nanjing 210044, China and College of Applied Meteorology, Nanjing University of Information Science a ...;Center for Computational Intelligence, School of Computing, De Montfort University, Leicester LE1 9BH, UK

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2012

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Abstract

Consistency and consensus measures are two important procedures employed in group decision making with multiplicative preference relations (MPRs). In this paper, we first establish the concept of individual consistency deviation degree between the original MPR and its optimal estimation. Then we develop a group consensus deviation degree optimization model (GCO Model) by minimizing the weighted arithmetic average of individual consistency deviation degrees. Our established theorems enlist the conditions for the existence of the optimal solution, the satisfactory solution, and non-inferior solution to the GCO Model. These results also provide an existence condition of redundant MPR in group decision making. Additionally, we show that the optimal value function of the GCO Model converges to 0, which implies that the consensus degree of DMs converges as the number of the decision makers increases indefinitely.