In this paper, we study interval-valued fuzzy probabilistic rough sets (IVF-PRSs) based on
multiple interval-valued fuzzy preference relations (IVFPRs) and consistency matrices, ie,
the multi-granulation interval-valued fuzzy preference relation probabilistic rough sets (MG-
IVFPR-PRSs). First, in the proposed study, we convert IVFPRs into fuzzy preference
relations (FPRs), and then construct the consistency matrix, the collective consistency matrix,
the weighted collective preference relations, and the group collective preference relation …

This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF)
probabilistic rough sets (MG-BVF-PRSs) models in multi-granulation BVF probabilistic
approximation space over two universes. Four types of MG-BVF-PRSs are established, by
the four different conditional probabilities of BVF event. For different constraints on
parameters, we obtain four kinds of each type MG-BVF-PRSs over two universes. To find a
suitable way of explaining and determining these parameters in each kind of each type MG …