Fuzzy functional dependencies and Bayesian networks

Springer Science and Business Media LLC - Tập 18 - Trang 56-66 - 2003
WeiYi Liu1,2, Ning Song3
1Department of Computer Science, Yunnan University, Kunming, P. R. China
2The Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, The Chinese Academy of Sciences, Beijing, P.R. China
3Department of Metallurgy, Kunming University of Science and Technology, Kunming, P.R. China

Tóm tắt

Bayesian networks have become a popular technique for representing and reasoning with probabilistic information. The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values. The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks. The connection is done through a set of methods that enable people to obtain the most information of independent conditions from fuzzy functional dependencies.

Tài liệu tham khảo

Heckerman D, Mamdani A, Wellman M P. Real-world applications of Bayesian networks.Communications of the ACM, 1995, 38(3): 25–30. Buntine W. A guide to the literature on learning probabilistic networks from data.IEEE Transactions on Knowledge and Data Engineering, 1996, 8(2): 195–210. Wuthrich B. Probalilistic knowledge bases.IEEE Transactions on Knowledge and Data Engineering, 1995, 7(5): 691–698. Jaeger M. On the complexity of inference about probabilistic relational models.Artificial Intelligence, 2000, 117(2): 297–308. Frisch A, Haddawy P. Anytime deduction for probabilistic logic.Artificial Intelligence, 1994, 69(1): 93–122. Nilsson N. Probabilistic logic.Artificial Intelligence, 1986, 28(1): 71–88. Baader F. A formal definition for the expressive power of knowledge representation languages. InProc. European Conf., Artificial Intelligence, Aiello L C (ed.), Stockholm, Sweden, 1990, pp. 53–58. Pearl J F. Propagation and structuring in belief networksArtificial Intelligence, 1986, 28(2): 241–288. Lauritzen S L. SpiegelhalterD J. Local computations with probabilities on graphical structures and their application to expert systems.Journal of Royal Statistical Society B, 1988, 50(2): 157–224. Ambrosio B D. Local expression ianguages for probabilistic dependence. InProc. 7th Conference on Uncertainty in Artificial Intelligence, Morgan Kaufman, San Mateo, Calif., 1991, pp.95–102. Heckerman D, Geiger D, Chickering D M. Learning Bayesian networks: The combination of knowledge and statistical data. Technical Report MSR-TR-94-09, Microsft Research, Advanced Technology Division, 1994. Cooper C. Computational complexity of probabilistic inference using Bayesian belief networks.Artificial Intelligence, 1990, 42(2): 394–405. Dagum P, Luby M. Approximately probabilistic reasoning in Bayesian belief networks in NP-hard.Artificial Intelligence, 1993, 60(1): 141–153. Dechter R. Decomposing a relation into a tree of binary relations.Journal of Computer and System Sciences, 1990, 41(1): 2–24. Wong S K M. An extended relational data model for probabilistic reasoning.Journal of Intelligent Information Systems, 1997, 9(2): 181–202. Butz C J, Wong S K M, Yao Y Y. On data and probabilistic dependencies. InIEEE Conf. Electrical and Computer Engineering, IEEE Press, Montreal, 1999, pp.1692–1697. Wong S K M, Buts C J, Wu D. On the implication problem for probabilistic conditional independence. Department of Computer Science, University of Regina, CA, Tech. Rep: CS-99-03, 1995. Getoor L, Koller D, Taskar B, Friedman N. Learning statistical models from relational data. InProc. AAAI 2000, Madison, 2000, pp.580–587. Malvestuto F M. A unique system for binary decomposition of database relations, probability distributions, and graphs.Information Sciences, 1992, 59(1): 21–52. Pearl J. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann Publishers, Inc., 1988, pp.1–293. Raju K V S V N, Majumdar A K. Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems.ACM Transactionson Database Systems, 1988, 13(1): 129–166. Tripathy R C, Saxena P C. Multivalued dependencies in fuzzy relational databases.Fuzzy Sets and Systems, 1990, 38(3): 267–280. Chen G Q. Normalization based on fuzzy functional dependency is a fuzzy relational data model.Information Systems, 1996, 21(3): 299–310. Sozat M I, Yazici A. A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations.Fuzzy Sets and Systems, 2001, 117(2): 161–183. Liao S Y, Wang H Q, Liu W Y. Functional dependencies with null values, fuzzy values, and crisp values.IEEE Transactions on Fuzzy Systems, 1999, 7(1): 97–103. Liu W Y. Fuzzy data dependencies and implication of fuzzy data dependencies.Fuzzy Sets and Systems, 1997, 92(3): 341–348. Larsen H L, Yager R R. Efficient computing of transitive ciosures.Fuzzy Sets and Systems, 1990, 38(1): 81–90. Tarjan R E, Leeuwen J V. Worst-case analysis of set union algorithms.J. ACM, 1984, 31(2): 245–281. Beeri C, Fagin R, Maier D, Yannakakis M. On the desirability of acyclic database schemes.Journal of the Association for Computing Machinery, 1983, 30(3): 479–513. Maier D. The Theory of Relational Databases. Rockville, Computer Science Press, 1983, pp.439–480. Ullman J D. Principles of Database Systems. Rockville, Computer Science Press, 1982, pp.166–208.