Fuzzy simple additive weighting method by preference ratio

Although simple additive weighting method (SAW) is the most popular approach for classical multiple attribute decision making (MADM), it is not practical any more if information is fuzzy. The existing methods of Fuzzy Simple Additive Weighting method (FSAW) apply defuzzification which distorts fuzzy numbers. Furthermore, most of the methods usually require lengthy and laborious manipulations. In this paper, we develop a new a fuzzy simple additive weighting method for multiple attribute decision making problems. To avoid defuzzification round off errors caused by multiplication or other arithmetic manipulations, fuzzy numbers are ranked prior to any fuzzy arithmetic in this method. The ranking is done by preference ratio concept which compares fuzzy numbers pairwise. Since this method eventually assigns crisp scores to alternatives, it is practical and more realistic. We also present three other algorithms for ranking or normalizing fuzzy numbers which are actually sub algorithms of the main method.