Affiliations: [a] College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P.R. China. [email protected]
Correspondence:
[†]
Address for correspondence: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, P.R. China
Note: [*] The authors thank the anonymous reviewers for their professional comments and valuable suggestions
Abstract: The notion of homomorphism, as an important tool for studying the relationship between information systems, has attracted a great deal of attention in recent years, and the authors tend to pay their attention to static information systems in the existing studies. In the present paper, we aim to study homomorphisms between fuzzy relation information systems (FRISs) in dynamic environments, where the terminology of dynamic refers to the fact that the involved information systems need to be updated with time due to the inflow of new information. To be more specific, we firstly examine properties of consistent functions with respect to fuzzy relations and construct homomorphisms between FRISs. Then, we develop incremental mechanisms of computing homomorphisms between dynamic FRISs and illustrate how to construct relation reducts of dynamic FRISs using homomorphisms. Lastly, the experimental results are employed to demonstrate that compressing dynamic FRISs can be simplified significantly with the proposed algorithms.
Keywords: Rough set, Consistent function, Fuzzy relation information system, Homomorphism
