Abstract
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.
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References
Kantardzic M. Data Mining: Concepts, Models, Methods, and Algorithms. Hoboken, NJ: John Wiley & Sons, 2011
Simovici D A, Tenney R L. Relational Database Systems. Orlando, FL: Academic Press, Inc., 1995
Kryszkiewicz M. Rough set approach to incomplete information systems. Information Sciences, 1998, 112(1): 39–49
Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338–353
Gau W L, Buehrer D J. Vague sets. IEEE Transactions on Systems, Man, and Cybernetics, 1993, 23(2): 610–614
Buckles B P, Petry F E. A fuzzy representation of data for relational databases. Fuzzy Sets and Systems, 1982, 7(3): 213–226
Ma ZM, Zhang F, Yan L, Cheng JW. Extracting knowledge from fuzzy relational databases with description logic. Integrated Computer-Aided Engineering, 2011, 18(2): 181–200
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, 401–416
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): 395–400
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, 562–565
Wei W, Cui J B, Liang J Y, Wang J H. Fuzzy rough approximations for set-valued data. Information Sciences, 2016, 360(9): 181–201
Zhong Y L. Attribute reduction of set-valued decision information system based on dominance relation. Journal of Interdisciplinary Mathematics, 2016, 19(3): 469–479
Zhang Z Y, Yang X B. Tolerance-based multigranulation rough sets in incomplete systems. Frontiers of Computer Science, 2014, 8(5): 753–762
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): 22–27
Motro A. Accommodating imprecision in database systems: issues and solutions. ACM SIGMOD Record, 1990, 19(4): 69–74
Ben-Ari M. Mathematical Logic for Computer Science. 3rd ed. London: Springer-Verlag, 2012
Acknowledgements
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).
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Shaobo Deng received his PhD from Key Laboratory of Intelligent Information, Institute of Computing Technology, Chinese Academy of Sciences, China in 2015. He is currently an associate professor in Nanchang Institute of Technology, China. His research interests include database theory and technology, Mathematical logic and Modal logic.
Sujie Guan received her MA from School of Information Engineering, Nanchang University, China in 2011. Her research interests include database theory and technology, Mathematical logic and Modal logic.
Min Li is a professor in the School of Information Engineering at Nanchang Institute of Technology, China. He received his PhD from the Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, China in 2014. His research interests include data mining, knowledge discovery in database with fuzzy and rough techniques.
Lei Wang is an associate professor in Nanchang Institute of Technology, China. He is also a CCF member. His research interests include rough set, granular computing and intelligent control.
Yuefei Sui is a professor in the Institute of Computing Technology, Chinese Academy of Sciences, China. His research interests include database theory and technology, mathematical logic and modal logic.
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Deng, S., Guan, S., Li, M. et al. Decomposition for a new kind of imprecise information system. Front. Comput. Sci. 12, 376–395 (2018). https://doi.org/10.1007/s11704-017-4436-2
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DOI: https://doi.org/10.1007/s11704-017-4436-2