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Abstract
When record sets become large, indexing becomes a required technique for speeding up querying. This holds for regular databases, but also for ` fuzzy' databases. In this paper we propose a novel indexing technique, supporting the querying of imperfect numerical data. A possibility based relational database setting is considered. Our approach is based on a novel adaptation of a B+-tree, which is currently still one of the most efficient indexing techniques for databases. The leaf nodes of a B+-tree are enriched with extra data and an extra tree pointer so that interval data can be stored and handled with them, hence the name Interval B+-tree (IBPT). An IBPT allows to index possibility distributions using a single index structure, offering almost the same benefits as a B+-tree. We illustrate how an IBPT index can be used to index fuzzy sets and demonstrate its benefits for supporting 'fuzzy' querying of 'fuzzy' databases. More specifically, we focus on the handling of elementary query criteria that use the so-called compatibility operator IS, which checks whether stored imperfect data are compatible with user preferences (or not).
Keywords
Indexing, Possibilistic databases, B+-tree

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MLA
De Tré, Guy, et al. “Indexing Possibilistic Numerical Data : The Interval B+-Tree Approach.” INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II, edited by Joao Paulo Carvalho et al., vol. 611, no. 2, Springer, 2016, pp. 305–16.
APA
De Tré, G., De Mol, R., & Bronselaer, A. (2016). Indexing possibilistic numerical data : the interval B+-tree approach. In J. P. Carvalho, M.-J. Lesot, U. Kaymak, S. Vieira, B. Bouchon-Meunier, & R. R. Yager (Eds.), INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II (Vol. 611, pp. 305–316). Switzerland: Springer.
Chicago author-date
De Tré, Guy, Robin De Mol, and Antoon Bronselaer. 2016. “Indexing Possibilistic Numerical Data : The Interval B+-Tree Approach.” In INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II, edited by Joao Paulo Carvalho, Marie-Jeanne Lesot, Uzay Kaymak, Susana Vieira, Bernadette Bouchon-Meunier, and Ronald R Yager, 611:305–16. Switzerland: Springer.
Chicago author-date (all authors)
De Tré, Guy, Robin De Mol, and Antoon Bronselaer. 2016. “Indexing Possibilistic Numerical Data : The Interval B+-Tree Approach.” In INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II, ed by. Joao Paulo Carvalho, Marie-Jeanne Lesot, Uzay Kaymak, Susana Vieira, Bernadette Bouchon-Meunier, and Ronald R Yager, 611:305–316. Switzerland: Springer.
Vancouver
1.
De Tré G, De Mol R, Bronselaer A. Indexing possibilistic numerical data : the interval B+-tree approach. In: Carvalho JP, Lesot M-J, Kaymak U, Vieira S, Bouchon-Meunier B, Yager RR, editors. INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II. Switzerland: Springer; 2016. p. 305–16.
IEEE
[1]
G. De Tré, R. De Mol, and A. Bronselaer, “Indexing possibilistic numerical data : the interval B+-tree approach,” in INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II, Eindhoven, The Netherlands, 2016, vol. 611, no. 2, pp. 305–316.
@inproceedings{7898169,
  abstract     = {{When record sets become large, indexing becomes a required technique for speeding up querying. This holds for regular databases, but also for ` fuzzy' databases. In this paper we propose a novel indexing technique, supporting the querying of imperfect numerical data. A possibility based relational database setting is considered. Our approach is based on a novel adaptation of a B+-tree, which is currently still one of the most efficient indexing techniques for databases. The leaf nodes of a B+-tree are enriched with extra data and an extra tree pointer so that interval data can be stored and handled with them, hence the name Interval B+-tree (IBPT). An IBPT allows to index possibility distributions using a single index structure, offering almost the same benefits as a B+-tree. We illustrate how an IBPT index can be used to index fuzzy sets and demonstrate its benefits for supporting 'fuzzy' querying of 'fuzzy' databases. More specifically, we focus on the handling of elementary query criteria that use the so-called compatibility operator IS, which checks whether stored imperfect data are compatible with user preferences (or not).}},
  author       = {{De Tré, Guy and De Mol, Robin and Bronselaer, Antoon}},
  booktitle    = {{INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, IPMU 2016, PT II}},
  editor       = {{Carvalho, Joao Paulo and Lesot, Marie-Jeanne and Kaymak, Uzay and Vieira, Susana and Bouchon-Meunier, Bernadette and Yager, Ronald R}},
  isbn         = {{978-3-319-40580-3}},
  issn         = {{1865-0929}},
  keywords     = {{Indexing,Possibilistic databases,B+-tree}},
  language     = {{eng}},
  location     = {{Eindhoven, The Netherlands}},
  number       = {{2}},
  pages        = {{305--316}},
  publisher    = {{Springer}},
  title        = {{Indexing possibilistic numerical data : the interval B+-tree approach}},
  url          = {{http://dx.doi.org/10.1007/978-3-319-40581-0_25}},
  volume       = {{611}},
  year         = {{2016}},
}

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