Affiliations: [a] School of Mathematics and Statistics, Hunan University of Commerce, Changsha, P.R. China | [b] School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China
Correspondence:
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Corresponding author. Bin Qin, School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P.R. China. E-mail: [email protected].
Abstract: A lattice-valued information system is an important model in the field of artificial intelligence and the notion of homomorphisms between lattice-valued information systems is a kind of tools to study data compression in a lattice-valued information system. This paper investigates invariant characterizations of information structures in a lattice-valued information system under homomorphisms based on data compression. Information structures in a lattice-valued information system is first proposed by using set vectors. Then, dependence and independence between information structures in the same lattice-valued information system is characterized by the inclusion degree. Finally, a complex massive lattice-valued information system can be compressed into a relatively small-scale lattice-valued information system by means of homomorphisms and it is proved that some characterizations of information structures in a lattice-valued information system under homomorphisms based on data compression are invariant, that is, some of the same data structures are obtained.
Keywords: Lattice-valued information system, granular computing, information granule, information structure, dependence, inclusion degree, characterization, homomorphism, data compression
