Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations
MetadataShow full item record
Consistency ascertainingHesitant multiplicative preference relations (HMPRs)Inconsistency repairingMissing valuesWeights derivation
Published version: Y. Xu... [et al.]. "Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations," in IEEE Transactions on Systems, Man, and Cybernetics: Systems, doi: [10.1109/TSMC.2021.3099862]
SponsorshipNational Natural Science Foundation of China (NSFC) 71871085; FEDER Funds provided in the National Spanish Project PID2019-103880RB-I00
This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models.