Abstract
We deal with the extension of division operation for flexible queries in relational databases where several graded notions are involved, such as the levels of certainty, of importance, or of fulfillment of a graded property, as well as fuzzy quantifiers. We address the case where both levels of fulfillment and levels of importance are present in the specification of a requirement. Furthermore, we consider the case where a level of fulfillment may be ill-known in the available data, which is expressed by a fuzzy-valued degree. We also show that quantifiers like most can be handled by a suitable weakening of the min operation in our extension.
This paper is a revised and extended version of a paper entitled “Find the items which certainly have (most of the) important characteristics to a sufficient degree” by the same authors, prepared for the 7th World Congress of the International Fuzzy Systems Associations (IFSA’97), Prague, June 25–29, 1997 (Proceedings published by Academia, Praha, Vol. 2, pp. 243–248).
Visiting scholar at IRIT, on leave from Information Science Department, Chiba-Keizai College, Japan.
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Bosc, P., Dubois, D., Pivert, O., and Prade, H. [1995] Fuzzy division for regular relational databases, in: Proceedings of the International Joint Conference of the 4th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE ‘85) and the 2nd International Fuzzy Engineering Symposium (IFES ‘85), Yokohama, Japan, March 20–24, 1995, pp. 729–734.
Bosc, P., Dubois, D., Pivert, O., and Prade, H. [1997] Flexible queries in relational databases — The example of the division operator, Theoretical Computer Science, 171, 281–302.
Bosc, P. and Liétard, L. [1995] On the division of relations with imprecise information, in: Fuzzy division for regular relational databases. in: Foundations and Applications of Possibility Theory (Proceedings of FART ‘85, Gent, Belgium, Dec. 13–15, 1995) ( G. de Gooman, Da Ruan, and E. E. Kerre, eds.), World Scientific, Singapore, pp. 287–294.
Bosc, P., Liétard, L., and Prade, H. [1996] On fuzzy queries involving fuzzy quantifiers, in: Proceedings of the ECAI Workshop on Uncertainty in Information Systems, Budapest, Hungary, Aug. 11–16, 1996, pp. 6–10. Extended version “An ordinal approach to the processing of fuzzy queries with flexible quantifiers” in: Applications of Uncertainty Formalisms (A. Hunter and S. Parsons, eds.), Lecture Notes in Computer Science, Springer, to appear.
Cubero, J. C., Medina, J. M., Pons, O., and Vila, M. A. [1994] The generalized selection: an alternative way for the quotient operations in fuzzy relational databases, in: Proceedings of the 5th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based System (IPMU ‘84), Paris, France, July 4–8, 1994, pp. 23–30.
Dubois, D. and Prade, H. [1986] Weighted minimum and maximum operations in fuzzy set theory, Information Sciences, 39, 205–210.
Dubois, D. and Prade, H. [1992] On the combination of evidence in various mathematical frameworks. In: Reliability Data Collection and Analysis ( J. Flamm and T. Luisi, eds.), Kluwer Academic Publishers, Dordrecht, pp. 213–241.
Dubois, D. and Prade, H. [1996] Semantics of quotient operators in fuzzy relational databases, Fuzzy Sets and Systems, 78, 89–93.
Mouaddib, N. [1994] Fuzzy identification in fuzzy databases. The nuanced relational division, International Journal of Intelligent Systems, 9, 461–473.
Nakata, M. [1996] Formulating division operators in fuzzy relational databases, in: Proceedings of the 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-BasedSystems (IPMU ‘86), Granada, Spain, July 1–5, 1996, pp.1277–1282. Extended version “Formulating fuzzy division operators in fuzzy relational databases” in: this volume.
Schweizer, B. and Sklar, A. [1983] Probabilistic Metric Spaces, North-Holland, Amsterdam.
Yager, R. R. [1994] Interpreting linguistically qualified propositions, International Journal Intelligent Systems, 9, 541–569.
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Dubois, D., Nakata, M., Prade, H. (2000). Extended Divisions for Flexible Queries in Relational Databases. In: Pons, O., Vila, M.A., Kacprzyk, J. (eds) Knowledge Management in Fuzzy Databases. Studies in Fuzziness and Soft Computing, vol 39. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1865-9_6
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DOI: https://doi.org/10.1007/978-3-7908-1865-9_6
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