On Partial Order Relations in Granular Computing

Information granularity is an approache to measuring uncertainty of an information system in granular computing. Partial order relations are often used to characterize the monotonicity of an uncertainty measure. In this paper, we focus on a generalized partial relation ≤´ with set-size character to information systems, and prove that three existing partial relations (≤₁, ≤₂ and ≤₃) are all its special cases. The analysis shows that the partial relation ≤´ presented appears to be well suited to characterize the essential natures of information granularity in granular computing.