During the last few years, more and more researchers have been applying IFSs to multi-attribute decision making under various different situations, and a lot of work has been done (Chen and Tan 1994; Hong and Choi 2000; Xu and Yager 2006; Boran et al. 2009; Xu 2010a, c; Zhao 2009; Zhao et al. 2010; Tan and Chen 2010; Wei 2010a; Xu and Xia 2012a; Xu and Cai 2010; Wu and Chen 2011, etc.). The con...