Notes on properties of the OWA weights determination model Gholam R. Amin * Department of Computer Science, Postgraduate Engineering Centre, Islamic Azad University of South Tehran Branch, Tehran 1418765663, Iran Received 4 January 2007; received in revised form 1 March 2007; accepted 2 March 2007 Available online 12 March 2007 Abstract This paper solves the recently open problem related to the OWA weights determination minimax model presented by Amin and Emrouznejad [Amin G. R., & Emrouznejad, A. (2006). An extended minimax disparity to determine the OWA operator weights. Computers & Industrial Engineering, 50, pp. 312–316]. So the contribution of this work is that it explains further the properties of the proposed OWA weights determination minimax model. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: OWA weights determination minimax model; Linear programming; Open problem 1. Introduction The concept of ordered weighted averaging (OWA) operator was introduced by Yager (1988, 1993). It has been used in applications of decision making, expert systems, neural networks, fuzzy system and control, (Filev & Yager, 1995; Pelaez & Dona, 2003; Yager & Kreinovich, 1999). It provides a general class of para- metric aggregation operators that includes the min, max, and average, and has shown to be useful for modeling many different kinds of aggregation problems. Several authors have provided interesting results on group deci- sion-making or social choice theory and multi-criteria decision-making with the help of fuzzy sets and OWA operator theory, (Chiclana, Herrera-Viedma, Herrera, & Alonso, 2007). The OWA operator affords a new information aggregation technique and has already aroused considerable research interest (Liu, 2006). For example, in machine scheduling optimization, the OWA operator is particularly useful because the amount of compensation can be adjusted freely, (Yager & Filev, 1994). An important issue related to the theory and application of OWA operators is the determination of the weights of the operators, (Amin & Emrouznejad, 2006; Fuller & Majlender, 2003; O’Hagan, 1988; Wang & Parkan, 2005). For generating the OWA operator weights Wang and Parkan (2005) proposed a linear pro- gramming model. By minimizing the maximum distance between any distinct pairs of weights instead of the adjacent weights, Amin and Emrouznejad (2006) were also contributed for determining of OWA operator weights. For further research the paper of those authors (Amin & Emrouznejad, 2006) appended an open 0360-8352/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.03.002 * Tel.: +98 (21) 66946032 5. E-mail address: G_Amin@azad.ac.ir Computers & Industrial Engineering 52 (2007) 533–538 www.elsevier.com/locate/dsw