Ordered weighted averaging in SAS: A MCDM application

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weighted averaging (OWA) operators of decision-making. OWA was originally introduced by Yager (1988) has gained much interest among researchers, hence many applications in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. To facilitate the use of OWA operator by SAS users, a code was implemented. An example is given to illustrate the features of the proposed macro. INTRODUCTION The ordered weighted averaging (OWA) operator which was initially introduced by Yager (1988) has attracted much interest among researcher. Since then several applications of the OWA operators are reported in different areas, such as decision making, expert systems, neural networks, group decision making and fuzzy systems and control. Many more applications of OWA are recently reported in multiple criteria decision making and preference ranking. OWA provides a general class of parameterized aggregation operators that include the min, max, average, and several other operators that recently introduced to the literature. The orness measure reflects the 'andlike' or 'orlike' aggregation result of an OWA operator, which is very important both in theory and applications. The extension of Yager’s orness concept to other aggregation operators has recently been focused by some researchers. O’Hagan(1988) suggested the problem of constraint nonlinear programming with a maximum entropy procedure, the solution is called a MEOWA (Maximum Entropy OWA) operator. Liu (2006) developed an OWA operator generating method with the equidifferent OWA operator, and discussed its properties; Wang and Parkan (2005) proposed a linear programming model with minimax disparity approach to get the OWA operator under desired orness level. Amin and Emrouznejad (2006) and Amin (2007) extended the minimax disparity approach using different optimization model. On the other hand, SAS is recognized as a one of the lead packages for statistical analysis and as a powerful tool for database management systems in many organizations. Many large industry including banks, pharmaceuticals, manufacturers, telecommunications companies, ... are suing SAS, all with the same basic needs to make better strategic decisions. There are wide rages of applications in SAS that the users recognized them as powerful tools in organizational management. For example the SAS/OR System has numerous optimization procedures which handle the standard problems such as linear and non-linear programming with all types of constraints, including integer, mixinteger and combinatorial optimization (SAS/OR User’s Guide: Mathematical Programming; 2007). These capabilities are exposed to the SAS users in a variety of places such as in procedures LP and NLP (Kearney; 1999) PROC OPTMODEL (Hughes and Kearney; 2007). In addition to the standard procedures available in SAS System applications such as neural network, simulation and control project management are introduced. Recently SAS/DEA and SAS/MALM macros were introduced by Emrouznejad (2000, 2002, and 2005) for measuring efficiency and productivity of Decision Making Units. This paper aims to introduce a new application in SAS System and with the aim for evaluation of a set of alternatives using OWA operators. OWA OPERATORS An OWA operator of dimension n is a mapping: R R F n → : that is associated with weighting vector [ ] n w w w W , , , 2 1 K = such that [ ] 1 , 0 ; 1 1 ∈ = ∑ = i n