Two new models for determining OWA operator weights q Ying-Ming Wang a, * , Ying Luo b , Xinwang Liu c a School of Public Administration, Fuzhou University, Fuzhou 350002, PR China b School of Management, Xiamen University, Xiamen 361005, PR China c School of Economics and Management, Southeast University, Nanjing 210096, PR China Received 24 September 2006; received in revised form 24 November 2006; accepted 12 December 2006 Available online 19 January 2007 Abstract The determination of ordered weighted averaging (OWA) operator weights is a very crucial issue of applying the OWA operator for decision making. This paper proposes two new models for determining the OWA operator weights. The weights determined by the new models do not follow a regular distribution and therefore make more sense than those obtained by other methods. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: OWA operator; Operator weights; Degree of orness 1. Introduction The ordered weighted averaging (OWA) operator defined by Yager (1988) provides a unified framework for decision making under uncertainty, in which different decision criteria such as maximax (optimistic), maximin (pessimistic), equally likely (Laplace) and Hurwicz criteria are characterized by different OWA operator weights. To apply the OWA operator for decision making, a very crucial issue is to determine its weights. O’Hagan (1988) was the first to determine OWA operator weights and suggested a maximum entropy method, which formulates the OWA operator weight problem as a constrained nonlinear optimization model with a predefined degree of orness as its constraint and the entropy as its objective function. The resultant weights are referred to as the maximum entropy weights. Fulle ´r and Majlender (2001) showed that the max- imum entropy model could be transformed into a polynomial equation that can be solved analytically. Fulle ´r and Majlender (2003) also suggested a minimum variance method to obtain the minimal variability OWA operator weights. Recently, Majlender (2005) extended the maximum entropy method to Re ´nyi entropy and proposed a maximal Re ´nyi entropy method that produces maximal Re ´nyi entropy OWA weights for a given level of orness. Liu and Chen (2004) put forward a parametric geometric method that could be used 0360-8352/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2006.12.002 q This research was supported by the National Natural Science Foundation of China (NSFC) under the Grant No.70301010. * Corresponding author. E-mail address: msymwang@hotmail.com (Y.-M. Wang). Computers & Industrial Engineering 52 (2007) 203–209 www.elsevier.com/locate/dsw