The consistent functions and reductions of fuzzy neighborhood systems

Neighborhood systems have been investigated extensively because of their applicability in granular computing. The consistent functions have been used to compare the structures of neighborhood systems. This paper is devoted to a further study of consistent functions and reductions of fuzzy neighborhood systems. Based on some equivalence relations on the universe, we propose a general method for constructing consistent functions. Some equivalent conditions for a function to be consistent are examined. In addition, the discernibility function of fuzzy neighborhood information systems is constructed which is used to compute all reductions of fuzzy neighborhood information systems. Accordingly, we make an analysis of fuzzy neighborhood systems based on three-way classification by using reductions.