Attribute weights determination models for consensus maximization in multiple attribute group decision-making

Abstract

Multiple attribute group decision making (MAGDM) is an important research field of decision science. A critical aspect of MAGDM is to determine the weights of attributes. In this paper, we study the MAGDM problem in which the attributes are given in real numbers or interval numbers, and the information about attribute weights is completely unknown or partially known. We first get the group opinion by fusing all individual opinion with each decision-makers' importance and introduce the deviation variable of each individual opinion and the group opinion. Then, we develop a quadratic programming model by means of minimizing the sum of all the deviation values, and a simple and straightforward formula for determining attribute weights can be derived from solving the developed models. We also establish a generalized model for solving MAGDM problems with partial weight information on attributes. In addition, we establish some similar models for MAGDM with interval attribute values. At last, we apply our models to a practical problem of a military unit purchasing new artillery weapons.

Keywords:

• multiple attribute group decision-making
• quadratic programming model
• deviation variable
• attribute weight

2000 Mathematics Subject Classification::

• 90B50
• 91B06

Acknowledgements

The author is very grateful to the anonymous referees for their constructive comments and suggestions that have led to an improved version of this paper. The work was partly supported by the National Science Fund for Distinguished Young Scholars of China (No. 70625005) and the National Natural Science Foundation of China (No. 71071161).