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Incremental Maintenance of Rough Fuzzy Set Approximations under the Variation of Object Set

100%

Zeng A. , Li T. , Zhang J. , Chen H.

Fundamenta Informaticae

2014

tom Vol. 132, nr 3

401--422

The lower and upper approximations in rough set theory will change dynamically over time due to the variation of the information system. Incremental methods for updating approximations in rough set theory and its extensions have received much attention recently. Most existing incremental methods have difficulties in dealing with fuzzy decision systems which decision attributes are fuzzy. This paper introduces an incremental algorithm for updating approximations of rough fuzzy sets under the variation of the object set in fuzzy decision systems. In experiments on 6 data sets from UCI, comparisons of the incremental and non-incremental methods for updating approximations are conducted. The experimental results show that the incremental method effectively reduces the computational time.

The Axiomatization of the Rough Set Upper Approximation Operations

88%

Liu G.-L.

2006

tom Vol. 69, nr 3

331-342

The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called, respectively, the lower and the upper approximation. There are at least two methods for the development of this theory, the constructive and the axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. This paper proposes a new matrix view of the theory of rough sets, we start with a binary relation and we redefine a pair of lower and upper approximation operators using the matrix representation. Different classes of rough set algebras are obtained from different types of binary relations. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of upper approximation operations guarantee the existence of certain types of binary relations(or matrices) producing the same operators. The upper approximation of the Pawlak rough sets, rough fuzzy sets and rough sets of vectors over an arbitrary fuzzy lattice are characterized by the same independent axiomatic system.