An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. A lattice-valued information system is the generalization of an information system. Its information structures are mathematical structures of the families of information granules granulated from its data sets. This paper explores information structures in a lattice-valued information system. The concept of information structures in a lattice-valued information system is first introduced by set vectors. Then, dependence, partial dependence, and independence between two information structures are proposed. Next, information distance between two information structures is studied. Moreover, properties of information structures are given. Finally, group, lattice, and mapping characterizations of information structures are obtained. These results will be helpful for building a framework of granular computing in lattice-valued information systems.
Lattice-valued information system Granular computing Information granule Information structure Dependence Information distance Inclusion degree Lattice Characterization
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The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of the paper. This work is supported by National Natural Science Foundation of China (11461005), Natural Science Foundation of Guangxi (2016GXNSFAA380045, 2016GXNSFAA380282, 2016GXNSFAA380286), Key Laboratory of Optimization Control and Engineering Calculation in Department of Guangxi Education, Special Funds of Guangxi Distinguished Experts Construction Engineering and Engineering Project of Undergraduate Teaching Reform of Higher Education in Guangxi (2017JGA179).
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Conflict of interest
All authors declare that there is no conflict of interests regarding the publication of this manuscript.
This article does not contain any studies with human participants or animals performed by any of the authors.
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