“…Since Hwang and Yoon (1981) proposed TOPSIS, it has been used and studied widely in the literature (Abo-Sinna and Amer, Chen, 2011Chen, , 2015Chen and Tsao, 2008;Cheng et al, 2003;Chu, 2002aChu, , 2002bLiu, 2003, 2009;Dymova et al, 2013aDymova et al, , 2015Joshi and Kumar, 2015;Krohling and Campanharo, 2011;Lai et al, 1994;Mahdevari, 2014;Mokhtarian, 2014;Rashid,2014;Wang and Elhag, 2006;Ye, 2010). Since the DM's judgments are often vague under risk and uncertain situations, crisp numbers may not be determined precisely; therefore, fuzzy values or interval values on TOPSIS methods have been proposed and discussed to solve problems under a fuzzy environment (Abo-Sinna and Amer, 2005;Agrawal et al, 1991;Chen, 2012Chen, , 2015Chen and Lee, 2010;Chen and Tsao, 2008;Cheng et al, 2003;Chu, 2002aChu, , 2002bLiu, 2003, 2009;Dymova et al, 2013bDymova et al, , 2015Jahanshahloo, 2009;Joshi and Kumar, 2015;Krohling & Campanharo, 2011;Lai et al, 1994;Tsaur, 2011;Wang and Elhag, 2006;Yue,2014).…”