“…However, in a complex decision environment, it may occur that the evaluation attributes cannot be determined, or the decision-maker is unable to perform the evaluation due to too many attributes, their own knowledge structure, or limited ability level ( Kropat et al, 2016 , Kropat and Weber, 2018 , Tirkolaee and Aydin, 2022 , Kalantari et al, 2022 , Goli et al, 2021 ). Thus, the decision-makers choose a very effective and simple method to compare alternatives two by two to determine the preference between alternatives, constructing a judgment matrix that reflects the preference relations (PRs) ( Orlovsky, 1978 , Grobelny et al, 2021 ). Currently, PRs can generally be described using multiplicative PRs (MPRs) ( Herrera et al, 2001 ), fuzzy PRs (FPRs) ( Orlovsky, 1978 ), linguistic PRs (LPRs) ( Dong et al, 2008 , Elibal and Özceylan, 2022 , Zhang et al, 2022 ), interval-valued FPRs (IVFPRs) ( Barrenechea et al, 2014 ) and intuitionistic FPRs (IFPRs) ( Xu, 2007 , Zhang et al, 2022 ).…”