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Homomorphisms Between Covering Approximation Spaces

The introduction of information system homomorphisms has made a substantial contribution to attribute reduction. However, the efforts made on homomorphisms are far from sufficient. This paper further investigates homomorphisms between covering approximation spaces. First, we introduce the concepts of upper and lower homomorphisms as well as homomorphisms in order to study the relationship between covering approximation spaces. Then we present the notions of covering approximation subspaces and product spaces. We also compress covering approximation spaces and covering information systems with the aim of attribute reduction. Afterwards, by utilizing the compressions of the original spaces and systems we compress the dynamic covering approximation spaces and dynamic covering information systems. Several illustrative examples are employed to demonstrate that the homomorphisms provide an effective approach for compressing covering approximation spaces and covering information systems.