Comments on A prioritization approach of non-reciprocal fuzzy preference relations and its extension

A recently published paper by Liu, Yang and Hu (2022) introduced a concept of non-reciprocal fuzzy preference relations (NrFPRs) and brought forward double-variance-based measuring formulas to compute additive con-sistency indices of NrFPRs and interval reciprocal fuzzy preference relations as well as built a double-variance -based minimization model with three parameters to acquire priority weight vectors from NrFPRs. This study employs five numerical illustrations to expose that some properties proposed by Liu, Yang and Hu (2022) are not true and the measuring formulas fail to obtain correct outcomes as well as the double-variance-based minimi-zation model is based on an incorrect assumption. NrFPRs are redefined as particular cases of fuzzy preference relations. An additive transitivity equation is established to define additive consistency of NrFPRs and a square deviation based formula is developed to calculate additive consistency indices of NrFPRs. A quadratic pro-gramming model is set up to acquire priority weight vectors with interval fuzzy elements from NrFPRs. A closed -form solution based approach is put forward to acquire optimal priority weight vectors from additively consistent NrFPRs.

Automated summary

This study introduces the concept of non-reciprocal fuzzy preference relations (NrFPRs) and presents measuring formulas and models to compute additive consistency indices and acquire priority weight vectors from NrFPRs. It identifies issues with previous properties and proposes redefined definitions and improved approaches.