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Homomorphism between ordered decision systems
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DOI：10.1007/s00500-018-3156-3.png)
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Abstract
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Communication between information systems is an important topic in granular computing. The notion of homomorphism is viewed as a basic tool to study this kind of problems. This work studies basic properties of ordered decision systems under homomorphism. We first review consistent function related to ordered relation and introduce the notion of consistent function related to a universal subset. The relationship between the two kinds of consistent functions is given. Then, the relationships between ordered rough approximations and their images are discussed under consistent functions. Finally, ordered decision systems are divided into two classes: consistent and inconsistent ordered decision systems. For each type of decision system, some of its basic homomorphic properties are presented. It is proved that attribute reductions in an original system and its image system are equivalent to each other under the condition of homomorphism in each type of ordered decision system.
Keywords:
Consistent functions
Relation mappings
Ordered decision systems
Homomorphism
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