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A note on communicating between information systems based on including degrees

In order to study the communication between information systems, Gong and Xiao (2010, International journal of general systems, 39, 189–206) proposed the concept of general relation mappings based on including degrees. Some properties and the extension for fuzzy information systems of the general relation mappings have been investigated there. In this paper, we point out by counterexamples that several assertions (Lemmas 3.1 and 3.2, Theorems 4.1 and 4.3) in the aforementioned work are not true in general.