Top

Published in:

2018 | OriginalPaper | Chapter

Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings

Authors : Olivier Pivert, Henri Prade

Published in: Scalable Uncertainty Management

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on possibility theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Inferring Quantitative Preferences: Beyond Logical Deduction

next chapter An Argumentative Recommendation Approach Based on Contextual Aspects

Then the attribute value, or more generally the disjunction of possible values is/are considered as fully possible, while any other value in the attribute domain is all the less possible as the certainty level is higher. In case of full certainty these other values are all impossible. This is a particular case of the certainty qualification of a fuzzy set, here reduced to a singleton, or in any case to a classical subset. There are other basic qualifications of a fuzzy set in possibility theory, for instance in terms of guaranteed possibility (rather than in terms of necessity as in certainty qualification), or which lead to enlarge the core, or to reduce the support of the fuzzy set, see [7] for the four canonic transformations; see also [20] for hybrid transformations combining enlargement with uncertainty.

For example, assume Peter has two ages, each with a certainty level, the levels being denoted by \(\alpha \) and \(\beta \) respectively. Then the FD name \(\rightarrow \) age is violated with a certainty degree that is equal to \(\min (\alpha ,\,\beta )\).

Arrazola, I., Plainfossé, A., Prade, H., Testemale, C.: Extrapolation of fuzzy values from incomplete data bases. Inf. Syst. 14(6), 487–492 (1989)CrossRef

Bertossi, L.E.: Database Repairing and Consistent Query Answering. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, San Rafael (2011)

Bosc, P., Pivert, O.: About projection-selection-join queries addressed to possibilistic relational databases. IEEE Trans. Fuzzy Syst. 13(1), 124–139 (2005)CrossRef

Bosc, P., Prade, H.: An introduction to the fuzzy set and possibility theory-based treatment of flexible queries and uncertain or imprecise databases. In: Motro, A., Smets, P. (eds.) Uncertainty Management in Information Systems. From Needs to Solutions, pp. 285–324. Kluwer Academic Publishers, Dordrecht (1997)CrossRef

De Tré, G., De Caluwe, R.M.M., Prade, H.: Null values in fuzzy databases. J. Intell. Inf. Syst. 30(2), 93–114 (2008)CrossRef

Dubois, D., Lang, J., Prade, H.: Automated reasoning using possibilistic logic: semantics, belief revision, and variable certainty weights. IEEE Trans. Knowl. Data Eng. 6, 64–71 (1994)CrossRef

Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets Syst. 84(2), 169–185 (1996)MathSciNetCrossRef

Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Gabbay, D.M., Smets, P. (eds.) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer, Dordrecht (1998)CrossRef

Dubois, D., Prade, H.: An overview of the asymmetric bipolar representation of positive and negative information in possibility theory. Fuzzy Sets Syst. 160(10), 1355–1366 (2009)MathSciNetCrossRef

10.

Dubois, D., Prade, H.: A glance at causality theories for artificial intelligence. In: A Guided Tour of Artifial Intelligence, vol. 1: Knowledge Representation, Reasoning and Learning. Springer (2018)

11.

Dubois, D., Prade, H., Schockaert, S.: Generalized possibilistic logic: foundations and applications to qualitative reasoning about uncertainty. Artif. Intell. 252, 139–174 (2017)MathSciNetCrossRef

12.

Hall, N., Köhler, H., Link, S., Prade, H., Zhou, X.: Cardinality constraints on qualitatively uncertain data. Data Knowl. Eng. 99, 126–150 (2015)CrossRef

13.

Ilyas, I.F., Chu, X.: Trends in cleaning relational data: consistency and deduplication. Found. Trends Databases 5(4), 281–393 (2015)CrossRef

14.

Imielinski, T., Lipski, W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)MathSciNetCrossRef

15.

Koehler, H., Leck, U., Link, S., Prade, H.: Logical foundations of possibilistic keys. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 181–195. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_13CrossRef

16.

Köhler, H., Link, S.: Qualitative cleaning of uncertain data. In: Mukhopadhyay, S., et al. (eds.) Proceedings of the 25th ACM International Conference on Information and Knowledge Management, CIKM 2016, Indianapolis, IN, USA, 24–28 October 2016, pp. 2269–2274. ACM (2016)

17.

Link, S., Prade, H.: Possibilistic functional dependencies and their relationship to possibility theory. IEEE Trans. Fuzzy Syst. 24(3), 757–763 (2016)CrossRef

18.

Link, S., Prade, H.: Relational database schema design for uncertain data. In: Mukhopadhyay, S., et al. (eds.) Proceedings of the 25th ACM International conference on Information and Knowledge Management, CIKM 2016, Indianapolis, 24–28 October, pp. 1211–1220 (2016)

19.

Meliou, A., Roy, S., Suciu, D.: Causality and explanations in databases. PVLDB 7(13), 1715–1716 (2014)

20.

González, A., Marín, N., Pons, O., Vila, M.A.: Qualification of fuzzy statements under fuzzy certainty. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds.) IFSA 2007. LNCS (LNAI), vol. 4529, pp. 162–170. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72950-1_17CrossRefMATH

21.

Pivert, O., Prade, H.: Detecting suspect answers in the presence of inconsistent information. In: Lukasiewicz, T., Sali, A. (eds.) FoIKS 2012. LNCS, vol. 7153, pp. 278–297. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28472-4_16CrossRef

22.

Pivert, O., Prade, H.: Querying uncertain multiple sources. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS (LNAI), vol. 8720, pp. 286–291. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11508-5_24CrossRef

23.

Pivert, O., Prade, H.: A certainty-based model for uncertain databases. IEEE Trans. Fuzzy Syst. 23(4), 1181–1196 (2015)CrossRef

24.

Pivert, O., Prade, H.: Database querying in the presence of suspect values. In: Morzy, T., Valduriez, P., Bellatreche, L. (eds.) ADBIS 2015. CCIS, vol. 539, pp. 44–51. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23201-0_6CrossRef

25.

Pivert, O., Prade, H.: Possibilistic conditional tables. In: Gyssens, M., Simari, G. (eds.) FoIKS 2016. LNCS, vol. 9616, pp. 42–61. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30024-5_3CrossRef

26.

Prade, H.: Lipski’s approach to incomplete information databases restated and generalized in the setting of Zadeh’s possibility theory. Inf. Syst. 9(1), 27–42 (1984)CrossRef

27.

Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incompleteuncertain information and vague queries. Inf. Sci. 34, 115–143 (1984)CrossRef

28.

Roblot, T.K., Link, S.: Possibilistic cardinality constraints and functional dependencies. In: Comyn-Wattiau, I., Tanaka, K., Song, I.-Y., Yamamoto, S., Saeki, M. (eds.) ER 2016. LNCS, vol. 9974, pp. 133–148. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46397-1_11CrossRef

29.

Suciu, D., Olteanu, D., Ré, C., Koch, C.: Probabilistic Databases. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, San Rafael (2011)MATH

30.

Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)MathSciNetCrossRef

Title: Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings
Authors: Olivier Pivert
Henri Prade
Publisher: Springer International Publishing
Book: Scalable Uncertainty Management
Print ISBN: 978-3-030-00460-6

Electronic ISBN: 978-3-030-00461-3

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-030-00461-3_30

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner