Decomposition for a new kind of imprecise information system
- 9 Downloads
In this paper, we first propose a new kind of imprecise information system, in which there exist conjunctions (∧’s), disjunctions (∨’s) or negations (¬’s). Second, this paper discusses the relation that only contains ∧’s based on relational database theory, and gives the syntactic and semantic interpretation for ∧ and the definitions of decomposition and composition and so on. Then, we prove that there exists a kind of decomposition such that if a relation satisfies some property then it can be decomposed into a group of classical relations (relations do not contain ∧) that satisfy a set of functional dependencies and the original relation can be synthesized from this group of classical relations. Meanwhile, this paper proves the soundness theorem and the completeness theorem for this decomposition. Consequently, a relation containing ∧’s can be equivalently transformed into a group of classical relations that satisfy a set of functional dependencies. Finally, we give the definition that a relation containing ∧’s satisfies a set of functional dependencies. Therefore, we can introduce other classical relational database theories to discuss this kind of relation.
Keywordsimprecise information systems decomposition composition soundness and completeness
Unable to display preview. Download preview PDF.
This work was partially supported by the Science and Technology Project of Jiangxi Provincial Department of Education (GJJ161109, GJJ151126), the National Natural Science Foundation of China (Grant Nos. 61363047, 61562061), and the Project of Science and Technology Department of Jiangxi Province (20161BBE50051, 20161BBE50050).
- 2.Simovici D A, Tenney R L. Relational Database Systems. Orlando, FL: Academic Press, Inc., 1995Google Scholar
- 7.Ma ZM, Zhang F, Yan L, Cheng JW. Extracting knowledge from fuzzy relational databases with description logic. Integrated Computer-Aided Engineering, 2011, 18(2): 181–200Google Scholar
- 8.Lu A, Ng W. Vague sets or intuitionistic fuzzy sets for handling vague data: Which one is better? In: Proceedings of International Conference on Conceptual Modeling. 2005, 401–416Google Scholar
- 9.Zheng X M, Xu T, Ma Z F. A vague data model and induction dependencies between attributes. Journal of Nanjing University of Aeronautics & Astronautics, 2001, 33(4): 395–400Google Scholar
- 10.Shen Q, Jiang Y L. Attribute reduction of multi-valued information system based on conditional information entropy. In: Proceedings of IEEE International Conference on Granular Computing. 2008, 562–565Google Scholar
- 14.Qiu T R, Liu Q, Huang H K. Granular computing based hierarchical concept capture algorithm in multi-valued information system. Pattern Recognition and Artifical Intelligence, 2009, 22(1): 22–27Google Scholar