A note on communicating between information systems based on including degrees

TL;DR

This paper critiques previous work on communication between information systems based on including degrees, highlighting inaccuracies in several key assertions through counterexamples.

Contribution

It identifies and corrects inaccuracies in prior assertions about general relation mappings in fuzzy information systems.

Findings

Several lemmas and theorems in the previous work are invalid in general.

Counterexamples demonstrate the inaccuracies in prior assertions.

The paper clarifies the limitations of previous theoretical results.

Abstract

In order to study the communication between information systems, Gong and Xiao [Z. Gong and Z. Xiao, Communicating between information systems based on including degrees, International Journal of General Systems 39 (2010) 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 (Lemma 3.1, Lemma 3.2, Theorem 4.1, and Theorem 4.3) in the aforementioned work are not true in general.