The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty

Abstract

The existing works usually assume that fuzzy preference relations (FPRs) exhibit additively reciprocal property. In this study, we investigate the situation that FPRs have no additively reciprocal property and address its implication to decision making under uncertainty. First, the considered situation is captured by proposing the novel concept of additively reciprocal property breaking (ARPB) for FPRs. It is proved that FPRs with ARPB, interval additive reciprocal preference relations (IARPRs) and intuitionistic fuzzy preference relations (IFPRs) are transformed each other. Second, the equivalence between FPRs with ARPR and additive reciprocal matrices (ARMs) is defined by keeping the inconsistency level unchanged. An optimization model is proposed to adjust an FPR without weak transitivity to an ARM with weak transitivity. Third, a novel decision making model is developed by considering weak transitivity of FPRs as the minimum requirement of rational choices. A new algorithm is elaborated on where decision information could be expressed as FPRs with ARPR, IARPRs and IFPRs, respectively. Finally, numerical results are reported to show the advantages of the developed model by comparing with the existing ones. The observations reveal that the concept of ARPB offers a novel understanding for uncertainty in decision information.