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A possibilistic view on set and multiset comparison

Antoon Bronselaer (UGent) , Axel Hallez (UGent) and Guy De Tré (UGent)
(2009) CONTROL AND CYBERNETICS. 38(2). p.341-366
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Abstract
Comparative evaluation operators for sets and multisets are proposed from a possibilistic point of view. In general, an evaluator estimates the possibility of (non) co-reference of two arbitrary (sub)-objects. Such operators can be used in a hierarchical possibilistic framework for finding co-referent objects with a complex structure. This paper first discusses properties of evaluators in general and continues with studying operators for sets and multisets, thereby making a clear distinction between hard and soft evaluators. Hard evaluators are based on evaluation of derived (multi)sets, while soft evaluators use a low level evaluator to incorporate co-reference at element level. The two important parts of such a soft evaluator are an injective element mapping and an aggregation function. An algorithm to provide the injective mapping is presented and discussed. For the aggregation step, ordered weighted conjunction is studied by introducing parameterized fuzzy quantifiers to calculate weight vectors. An advanced learning strategy is introduced to train the optimal parameter matrix.
Keywords
evaluator, co-reference, multisets, sets, RECORD-LINKAGE, BAGS

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Chicago
Bronselaer, Antoon, Axel Hallez, and Guy De Tré. 2009. “A Possibilistic View on Set and Multiset Comparison.” Ed. Guy De Tré and Slawomir Zadrozny. Control and Cybernetics 38 (2): 341–366.
APA
Bronselaer, A., Hallez, A., & De Tré, G. (2009). A possibilistic view on set and multiset comparison. (G. De Tré & S. Zadrozny, Eds.)CONTROL AND CYBERNETICS, 38(2), 341–366. Presented at the Special Session on the Application of Fuzzy Logic and Soft Computing in Flexible Quering held at the IFSA 2007 World Congress.
Vancouver
1.
Bronselaer A, Hallez A, De Tré G. A possibilistic view on set and multiset comparison. De Tré G, Zadrozny S, editors. CONTROL AND CYBERNETICS. 2009;38(2):341–66.
MLA
Bronselaer, Antoon, Axel Hallez, and Guy De Tré. “A Possibilistic View on Set and Multiset Comparison.” Ed. Guy De Tré & Slawomir Zadrozny. CONTROL AND CYBERNETICS 38.2 (2009): 341–366. Print.
@article{748943,
  abstract     = {Comparative evaluation operators for sets and multisets are proposed from a possibilistic point of view. In general, an evaluator estimates the possibility of (non) co-reference of two arbitrary (sub)-objects. Such operators can be used in a hierarchical possibilistic framework for finding co-referent objects with a complex structure. This paper first discusses properties of evaluators in general and continues with studying operators for sets and multisets, thereby making a clear distinction between hard and soft evaluators. Hard evaluators are based on evaluation of derived (multi)sets, while soft evaluators use a low level evaluator to incorporate co-reference at element level. The two important parts of such a soft evaluator are an injective element mapping and an aggregation function. An algorithm to provide the injective mapping is presented and discussed. For the aggregation step, ordered weighted conjunction is studied by introducing parameterized fuzzy quantifiers to calculate weight vectors. An advanced learning strategy is introduced to train the optimal parameter matrix.},
  author       = {Bronselaer, Antoon and Hallez, Axel and De Tr{\'e}, Guy},
  editor       = {De Tr{\'e}, Guy and Zadrozny, Slawomir},
  issn         = {0324-8569},
  journal      = {CONTROL AND CYBERNETICS},
  keyword      = {evaluator,co-reference,multisets,sets,RECORD-LINKAGE,BAGS},
  language     = {eng},
  location     = {Cancun, MEXICO},
  number       = {2},
  pages        = {341--366},
  title        = {A possibilistic view on set and multiset comparison},
  volume       = {38},
  year         = {2009},
}

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