Showing papers on "Rough set published in 1987"

Rough approximation of shapes in pattern recognition

Abstract: The paper approaches the nature of a feature recognition process through the description of image features in terms of the rough sets. Since the basic condition for representing images must be satisfied by any recognition result, elementary features are defined as equivalence classes of possible occurrences of specific fragments existing in images. The names of the equivalence classes (defined through specific numbers of objects and numbers of background parts covered by a window) constitute the best lower approximation of window contents (i.e., names of recognized features). The best upper approximation is formed by the best lower approximation, its attributes, and parameters, all referenced to the object fragments situated in the window. The rough approximation of shapes is resistant to accidental changes in the width of contours and lines and to small discontinuities and, in general, to possible positions or changes in shape of the same feature. The rough sets are utilized also on the level of image processing for noiseless image quantization.

Decision tables: A rough set approach

Abstract: W: Bulletin of the European Association for Theoretical Computer Science (EATCS), 33:85-95, 1987

Logic of Approximation Reasoning

Abstract: An algebraic and set-theoretical approach to approximation reasoning as proposed in [10] and [5] leads to a formulation of a class of first order logics. They are certain intermediate logics equipped with approximation operators dt for t e T — where (T, ≤) is a poset establishing a type of logic under consideration — and with modal connectives Ct of possibility and It of necessity, t e T and possibly with CT and IT. Their semantics is based on the idea that a set of objects to be recognized in a process of an approximation reasoning is approximated by means of a family of sets covering this set and by their intersection. Approximating sets with equivalence classes of equivalence relations, as connected with Pawlak's rough sets methods (see [8], [7], [12], [13]) is an additional tool. The main task of this paper is to formulate and prove the completeness theorem for the logics under consideration. For that purpose a theory of plain semi-Post algebras as introduced and developed in [3] has been applied. These algebras replace more complicated semi-Post algebras occurring in [10].