A note on "communicating between information systems"

This note is an amendment to a paper by Wang et al. [C. Wang, C. Wu, D. Chen, Q. Hu, and C. Wu, Communicating between information systems, Information Sciences 178 (2008) 3228-3239]. To study the communication between two information systems, Wang et al. proposed two concepts of type-1 and type-2 consistent functions. Some good properties of consistent functions and induced relation mappings have been investigated there. In this paper, we provide an improvement of the aforementioned work by disclosing the symmetric relationship between type-1 and type-2 consistent functions. We present more properties of consistent functions and induced relation mappings and correct several deficient assertions in the original work. In particular, we unify and extend type-1 and type-2 consistent functions into the so-called neighborhood-consistent functions. This provides a convenient means for studying the communication between information systems based on various neighborhoods.