Multi-granular Perspectives on Covering

TL;DR

This paper introduces a multi-granular perspective on covering models in granular computing, exploring transformations among different granular worlds and providing relational interpretations of covering-based rough approximation operators.

Contribution

It presents a novel multi-granular framework for covering models, including transformations among granular worlds and axiomatizations of rough approximation operators.

Findings

Defined intersection and union of covering blocks as granules at different levels

Analyzed transformations among granular worlds at various abstraction levels

Provided relational interpretations and axiomatizations of covering-based rough operators

Abstract

Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as granules to form granular worlds at different abstraction levels, respectively, and transformations among these different granular worlds are also discussed. As an application of the presented multi-granular perspective on covering, relational interpretation and axiomization of four types of covering based rough upper approximation operators are investigated, which can be dually applied to lower ones.