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Knowledge Reduction in Random Incomplete Decision Tables via Evidence Theory

Wu W. Z.

Fundamenta Informaticae

2012

Vol. 115, nr 2/3

203-218

Statisticians and database users often encounter the problem of missing or imprecise data obtained by a random experiment. Such a data set is called a random incomplete information table. In this paper, we study knowledge reduction in random incomplete information tables and random incomplete decision tables by using a hybrid model based on the rough set theory and the Dempster- Shafer theory of evidence. The concepts of random belief reducts and random plausibility reducts in random incomplete information tables and random incomplete decision tables are introduced. The relationships among the lower approximation reduct, the upper approximation reduct, the random belief reduct, the random plausibility reduct, and the classical reduct in random incomplete decision tables are examined.

A new version of the multivalued Fatou lemma

Piccinini L.

Journal of Applied Analysis

1998

Vol. 4, nr 2

231-244

H. Kudo introduced a notion of convergence of a sequence Bn of sub-σ-fields. We emphasize a connection with Mosco-convergence of associated subspaces LpE (Bn) where E is a separable Banach space with separable dual. This enables us to study the convergence of conditional expectation sequences of random sets and therefore to obtain a new version of the multivalued Fatou lemma.