Representing uncertainty on set-valued variables using belief functions

被引:33
作者
Denoeux, Thierry [1 ]
Youne, Zoulficar [1 ]
Abdallah, Fahed [1 ]
机构
[1] Ctr Rech Royallieu, CNRS, UTC, HEUDIASYC, F-60205 Compiegne, France
关键词
Dempster-Shafer theory; Evidence theory; Conjunctive knowledge; Lattice; Uncertain reasoning; Multi-label classification; RULE; CLASSIFICATION; PROBABILITY; COMBINATION; MODEL;
D O I
10.1016/j.artint.2010.02.002
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variable X on a domain Omega is a variable taking zero, one or several values in Omega. While defining mass functions on the frame 2(2 Omega) is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a restricted family of subsets of 2(Omega) that is closed under intersection and has a lattice structure. Using recent results about belief functions on lattices, we show that most notions from Dempster-Shafer theory can be transposed to that particular lattice, making it possible to express rich knowledge about X with only limited additional complexity as compared to the single-valued case. An application to multi-label classification (in which each learning instance can belong to several classes simultaneously) is demonstrated. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:479 / 499
页数:21
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