Fuzzy functional dependencies and Bayesian networks

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.