Abstract
An axiomatic system for fuzzy functional dependencies is introduced. The main novelty of the system is that it is not based on the transitivity rule like all the others, but it is built around a simplification rule which allows the removal of redundancy. The axiomatic system presented here is shown to be sound and complete.
Partially supported by Spanish project TIN07-65819.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Armstrong, W.W.: Dependency structures of data base relationships. In: Proc. IFIP Congress, pp. 580–583. North-Holland, Amsterdam (1974)
Abiteboul, S., Agrawal, R., Bernstein, P.A., et al.: The Lowell database research self-assessment. Commun. ACM 48(5), 580–583 (2005)
Baldwin, J.F.: Knowledge engineering using a fuzzy relational inference language. In: Proc. IFAC Conf. on Fuzzy Information, Knowledge Representation, and Decision Processes, Marseille, France, pp. 15–23 (1983)
Belohlávek, R., Vychodil, V.: Basic Algorithm for Attribute Implications and Functional Dependencies in Graded Setting. Int. J. Found. Comput. Sci. 19(2), 297–317 (2008)
Bernstein, P.A., Swenson, J.R.: A unified approach to functional dependencies and relations. In: Proc. ACM SIGMOD Conf., San Jose, CA, pp. 237–245 (1974)
Buckles, B.P., Petry, F.E.: Uncertainty models in information and database systems. J. Inform. Sci. 11, 77–87 (1985)
Cabrera, I.P., Cordero, P., Gutiérrez, G., Martínez, J., Ojeda-Aciego, M.: Fuzzy congruence relations on nd-groupoids, Int. J. on Computer Mathematics (to appear, 2009)
Codd, E.F.: The relational model for database management: Version 2. Addison Wesley, Reading (1990)
Cordero, P., Enciso, M., de Guzmán, I.P., Mora, A.: Slfd logic: Elimination of data redundancy in knowledge representation. In: Garijo, F.J., Riquelme, J.-C., Toro, M. (eds.) IBERAMIA 2002. LNCS (LNAI), vol. 2527, pp. 141–150. Springer, Heidelberg (2002)
Cordero, P., Mora, A., Enciso, M., Aguilera, G., de Guzmán, I.P.: Reasoning about Fuzzy Functional Dependencies. In: ESTYLF 2008, pp. 121–126 (2008)
Cubero, J.C., Vila, M.A.: A new definition of fuzzy functional dependency in fuzzy relational databases. Internat. J. Intell. Systems 9(5), 441–448 (1994)
Fagin, R.: Functional dependencies in a relational database and propositional logic. IBM J. of Research and Development 21(6), 534–544 (1977)
Giardina, C., Sack, I., Sinha, D.: Fuzzy Field Relational Database. Report 8332, Elect. Engng. and Computer Science Dept., Stevens Institute of Technology, Hoboken, NJ (1983)
Guan, J.W., Bell, D.A.: Rough computational methods for information systems. Artificial Intelligence 1051(2), 77–103 (1998)
Jaeschke, G., Schek, H.-J.: Remarks on the algebra of non first normal form relations. In: Proceedings of the ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 124–138. ACM Press, New York (1982)
Mora, A., Enciso, M., Cordero, P., de Guzmán, I.P.: The functional dependence implication problem: optimality and minimality. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) CAEPIA/TTIA 2003. LNCS, vol. 3040, pp. 136–146. Springer, Heidelberg (2004)
Mora, A., Aguilera, G., Enciso, M., Cordero, P., de Guzmán, I.P.: A new closure algorithm based in logic: SLFD-Closure versus classical closures. Inteligencia Artificial, Revista Iberoamericana de IA 31(10), 31–40 (2006)
Prade, H.: The connection between Lipskios approach to incomplete information data bases and Zadeh’s Possibility Theory. In: Proc. Int. Conf. Systems Meth., pp. 402–408 (1982)
Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries. Information Sciences 34, 115–143 (1984)
Raju, H.V.S.V.N., Mazumdar, A.K.: Fuzzy dependencies and losless join descomposition of fuzzy relational database systems. ACM Transaction of Database Systems 13(2), 129–166 (1988)
Savnik, I., Flach, P.A.: Bottom-up induction of functional dependencies from relations. In: Proc. of AAAI 1993 Workshop: Knowledge Discovery in Databases, pp. 174–185 (1993)
Sozat, M.I., Yazici, A.: A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations. Fuzzy Sets and Systems 117(2), 161–181 (2001)
Tyagi, B.K., Sharfuddin, A., Dutta, R.N., Tayal, D.K.: A complete axiomatization of fuzzy functional dependencies using fuzzy function. Fuzzy Set and Systems 151(2), 363–379 (2005)
Ullman, J.D.: Database and knowledge-base systems. Computer Science Press (1988)
Bělohlávek, R., Vychodil, V.: Data Tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases. In: Li Lee, M., Tan, K.-L., Wuwongse, V. (eds.) DASFAA 2006. LNCS, vol. 3882, pp. 644–658. Springer, Heidelberg (2006)
Yahia, S.B., Ounalli, H., Jaoua, A.: An Extension of Classical Functional Dependency: Dynamic Fuzzy Functional Dependency. Inf. Sci. 119(3-4), 219–234 (1999)
Zadeh, L.: Is there a need for fuzzy logic? Information Science 178(13), 2751–2779 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cordero, P., Enciso, M., Mora, A., de Guzmán, I.P. (2009). A Complete Logic for Fuzzy Functional Dependencies over Domains with Similarity Relations. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds) Bio-Inspired Systems: Computational and Ambient Intelligence. IWANN 2009. Lecture Notes in Computer Science, vol 5517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02478-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-02478-8_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02477-1
Online ISBN: 978-3-642-02478-8
eBook Packages: Computer ScienceComputer Science (R0)