“…On the other hand, because of complexity of decision problems and the limited ability of human pairwise comparisons, DMs may be unable to provide their preferences over some pairs of decision alternatives. As such, incomplete judgments are resulted and decision making problems with incomplete preference relations have been received more and more attention in recent years (Mattila & Virtanen, 2015;Punkka & Salo, 2013;Wang & Li, 2015). The consistency of preference relations is a crucial foundation for estimating missing values and obtaining a reasonable and reliable decision result (Brunelli, Canal, & Fedrizzi, 2013;Brunelli & Fedrizzi, 2015;Kou, Ergu, & Shang, 2014).…”