Homomorphism between ordered decision systems
- 39 Downloads
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.
KeywordsConsistent functions Relation mappings Ordered decision systems Homomorphism
This work was supported by the National Natural Science Foundation of China under Grants 61572082, 61673396, and 61473111, the Foundation of Educational Committee of Liaoning Province (LZ2016003), the Natural Science Foundation of Liaoning Province (20170540012, 20170540004).
Compliance with ethical standards
Conflict of interest
Authors declare that they have no conflict of interest.
Human and animal rights disclosure
This article does not contain any studies with human participants or animals performed by any of the authors.
- Grzymala-Busse JW (1986) Algebraic properties of knowledge representation systems. In: Proceedings of the ACM SIGART international symposium on methodologies for intelligent systems, Knoxville, pp 432–440Google Scholar
- Sun L, Zhang X, Xu J, Wang W, Liu R (2018) A gene selection approach based on the fisher linear discriminant and the neighborhood rough set. Bioengineered 9(1):144–151. https://doi.org/10.1080/21655979.2017