A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

A consistency model for group decision making problems with interval multiplicative preference relations

“…For example, Liu et al [22] introduced an incomplete IMPR and gave the definitions of consistent and acceptable incomplete ones. In addition, they proposed a goal programming model to complement the acceptable incomplete one.…”

D-CFPR: D numbers extended consistent fuzzy preference relations

“…According to previous studies, the preference relation can be divided into two categories. The first one is multiplicative preference relation [2,3,4,5] which is subjected to the multiplicative reciprocal, i.e. a ij ×a ji = 1.…”

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

“…In reality, the decision-maker is sometimes unable or unwilling to provide his/her opinions over some alternatives due to insufficient information or limited expertise, especially in face of a large number of criteria or alternatives. In this situation, an incomplete comparison matrix is resulted (Alonso et al, , 2010Chiclana et al, 2008Chiclana et al, , 2009aFedrizzi & Giove , 2007;Gong, 2008;Herrera-Viedma et al, 2007;Liu, Zhang, & Wang, 2012;Liu, Pan, Xu, & Yu , 2012;Xu, 2004Xu, , 2012Xu, Li, & Wang, 2014). MCDM with incomplete comparison matrices have been receiving increasing attention and many different methods have been developed to estimate missing or unknown values for incomplete additive reciprocal comparison matrices (Alonso et al, , 2010Chiclana et al, 2009a;Gong, 2008;Herrera-Viedma et al, 2007;Liu, Pan, Xu, & Yu , 2012;Xu, 2004).…”