Fuzzy rough set with inconsistent bipolarity information in two universes and its applications

In the paper (Han et al. in IEEE Trans Fuzzy Syst 23:2358–2370, 2015), we proposed the bipolar-valued rough fuzzy set in one universe, which is an inevitable improvement by introducing inconsistentbipolarity to rough set. However, the bipolar-valued rough fuzzy set in one universe still has the limitations to complex practical problems. This motives us to propose the generalized concept of bipolar-valued fuzzy rough set in two universes, in which, inconsistentbipolarity is introduced into the crisp approximation space for the first time, and furthermore, two universes are considered to reflect the interrelations among different sources’ inconsistentbipolarity information. Comparing with other existing fuzzy rough set models, in syntax, the new one generalizes the existing ones. And most importantly, in semantics, the new one firstly considering the inconsistentbipolarity information, which is important in practice. Based on the new concept, two methods to the decision-making problems with inconsistent fuzzy bipolarity information are proposed, together with their applications. The comparison study with other existing rough set related methods highlights the necessity of our study, which provides a new inconsistent fuzzy bipolarity perspective to rough set theory and related applications.