TY - JOUR
T1 - Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations
AU - Xu, Gai Li
AU - Wan, Shu Ping
AU - Wang, Feng
AU - Dong, Jiu Ying
AU - Zeng, Yifeng
PY - 2016/4/15
Y1 - 2016/4/15
N2 - In group decision making (GDM) with intuitionistic fuzzy preference relations (IFPRs), the consistency and consensus are two key issues. This paper develops a novel method for checking and improving the consistency of individual IFPRs and the consensus among experts. To measure the consistency degree of IFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IFPR with unacceptable consistency, a mathematical programming approach is developed to improve its consistency. To evaluate the consensus degree among experts, a consensus measure is presented by the proximity degree between one expert and other experts. When several individual IFPRs are unacceptable consistent or consensus is unacceptable, a goal program is built to improve the consistency and consensus simultaneously. By the consistency and proximity degrees of individual IFPRs, experts' objective weights are determined. Combining the experts' subjective weights, the experts' comprehensive weights are derived. Then, an intuitionistic fuzzy geometric weighted mean (IFGWM) operator is proposed to integrate individual IFPRs into a collective one. Moreover, an attractive property is proved that the collective IFPR is acceptable consistent if all individual IFPRs are acceptable consistent. Two examples are provided to illustrate the validity of the proposed method.
AB - In group decision making (GDM) with intuitionistic fuzzy preference relations (IFPRs), the consistency and consensus are two key issues. This paper develops a novel method for checking and improving the consistency of individual IFPRs and the consensus among experts. To measure the consistency degree of IFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IFPR with unacceptable consistency, a mathematical programming approach is developed to improve its consistency. To evaluate the consensus degree among experts, a consensus measure is presented by the proximity degree between one expert and other experts. When several individual IFPRs are unacceptable consistent or consensus is unacceptable, a goal program is built to improve the consistency and consensus simultaneously. By the consistency and proximity degrees of individual IFPRs, experts' objective weights are determined. Combining the experts' subjective weights, the experts' comprehensive weights are derived. Then, an intuitionistic fuzzy geometric weighted mean (IFGWM) operator is proposed to integrate individual IFPRs into a collective one. Moreover, an attractive property is proved that the collective IFPR is acceptable consistent if all individual IFPRs are acceptable consistent. Two examples are provided to illustrate the validity of the proposed method.
UR - http://www.scopus.com/inward/record.url?scp=84955599329&partnerID=8YFLogxK
U2 - 10.1016/j.knosys.2015.12.007
DO - 10.1016/j.knosys.2015.12.007
M3 - Article
AN - SCOPUS:84955599329
SN - 0950-7051
VL - 98
SP - 30
EP - 43
JO - Knowledge-Based Systems
JF - Knowledge-Based Systems
ER -