Advanced search
1 file | 255.72 KB Add to list

Comparison of sets and multisets

Axel Hallez (UGent) , Antoon Bronselaer (UGent) and Guy De Tré (UGent)
Author
Organization
Abstract
The comparison of sets of objects is a research topic with applications in diverse fields such as computer science, biology and psychology. Since the introduction of the Jaccard index, many techniques have been proposed. This paper aims at extending an existing framework of comparison indices for sets. Firstly, the novel indices account for similarities between elements, rather than identity of elements as is the case for existing techniques. As a result, a richer framework of comparison indices is obtained. The use of fuzzy quantifiers in this framework is shown. Secondly, the machinery for sets is extended to the case of multisets, which results in two classes of comparison indices. The first class considers each element instance as a separate element, while the second class considers groups of elements instances as an atomic entity. The number of instances is then a property of this group, that is taken into account when calculating similarity between element groups.
Keywords
comparison indices, Sets, multisets, NON-CARDINAL DATA, FUZZY BAGS, CONTEXT

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 255.72 KB

Citation

Please use this url to cite or link to this publication:

MLA
Hallez, Axel, et al. “Comparison of Sets and Multisets.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 17, no. suppl. 1, 2009, pp. 153–72, doi:10.1142/S0218488509006078.
APA
Hallez, A., Bronselaer, A., & De Tré, G. (2009). Comparison of sets and multisets. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 17(suppl. 1), 153–172. https://doi.org/10.1142/S0218488509006078
Chicago author-date
Hallez, Axel, Antoon Bronselaer, and Guy De Tré. 2009. “Comparison of Sets and Multisets.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17 (suppl. 1): 153–72. https://doi.org/10.1142/S0218488509006078.
Chicago author-date (all authors)
Hallez, Axel, Antoon Bronselaer, and Guy De Tré. 2009. “Comparison of Sets and Multisets.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 17 (suppl. 1): 153–172. doi:10.1142/S0218488509006078.
Vancouver
1.
Hallez A, Bronselaer A, De Tré G. Comparison of sets and multisets. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2009;17(suppl. 1):153–72.
IEEE
[1]
A. Hallez, A. Bronselaer, and G. De Tré, “Comparison of sets and multisets,” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 17, no. suppl. 1, pp. 153–172, 2009.
@article{734606,
  abstract     = {{The comparison of sets of objects is a research topic with applications in diverse fields such as computer science, biology and psychology. Since the introduction of the Jaccard index, many techniques have been proposed. This paper aims at extending an existing framework of comparison indices for sets. Firstly, the novel indices account for similarities between elements, rather than identity of elements as is the case for existing techniques. As a result, a richer framework of comparison indices is obtained. The use of fuzzy quantifiers in this framework is shown. Secondly, the machinery for sets is extended to the case of multisets, which results in two classes of comparison indices. The first class considers each element instance as a separate element, while the second class considers groups of elements instances as an atomic entity. The number of instances is then a property of this group, that is taken into account when calculating similarity between element groups.}},
  author       = {{Hallez, Axel and Bronselaer, Antoon and De Tré, Guy}},
  issn         = {{0218-4885}},
  journal      = {{INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS}},
  keywords     = {{comparison indices,Sets,multisets,NON-CARDINAL DATA,FUZZY BAGS,CONTEXT}},
  language     = {{eng}},
  number       = {{suppl. 1}},
  pages        = {{153--172}},
  title        = {{Comparison of sets and multisets}},
  url          = {{http://dx.doi.org/10.1142/S0218488509006078}},
  volume       = {{17}},
  year         = {{2009}},
}

Altmetric
View in Altmetric
Web of Science
Times cited: