A prioritization approach of non-reciprocal fuzzy preference relations and its extension. (June 2022) - Liu, Fang; Yang, Hui; Hu, Yuan-Kai
Highlights: A double variance consistency index is proposed for NrFPRs. A novel additive consistency index of IARMs is constructed. An optimization-based prioritization method is reported for NrFPRs. A new interval-valued prioritization method is given for IARMs. Abstract: In decision making problems, preference relations are the widely used tools to simulate the opinions of decision makers (DMs). It is important to elicit priorities from a preference relation in order to reach an optimal solution. In this paper, we propose an optimization-based method to derive the priority vector from a fuzzy preference relation (FPR) without additively reciprocal property (ARP). First, the concept of non-reciprocal fuzzy preference relations (NrFPRs) is used to characterize the case of FPRs without ARP. An interval additive reciprocal matrix (IARM) is decomposed into two NrFPRs. Second, the variance similarity measure is proposed to quantify the similarity degree of two column/row vectors of NrFPRs. A double variance consistency index is constructed to measure the inconsistency degree of NrFPRs. An optimization-based model is proposed to elicit the priority vector from NrFPRs. Some interesting properties are addressed to show the effectiveness of the proposed approach. Third, the proposed prioritization method is extended to derive priorities from IARMs. Some comparisons with the existing prioritization methods of IARMs are reported using numerical examples. The observations reveal that the uncertainty exhibiting in IARMs can be captured by NrFPRs. Some decision-making models with IARMs could be revisited using the proposed method for NrFPRs.