On the Extension of Rough Sets under Incomplete Information
نویسندگان
چکیده
The rough set theory, based on the indiscernibility relation, is not useful for analysing incomplete information. Therefore, we introduce two generalizations of this theory, besides the well known one based on tolerance relations. The rst proposal is based on non symmetric similarity relations, while the second one uses valued tolerance relation. Both approaches provide more informative results than the previously known approach employing simple tolerance relation.
منابع مشابه
A New Extension Model of Rough Sets Under Incomplete Information
The classical rough set theory based on complete information systems stems from the observation that objects with the same characteristics are indiscernible according to available information. With respect to upper-approximation and lower-approximation defined on an indiscernibility relation it classifies objects into different equivalent classes. But in some cases such a rigid indiscernibility...
متن کاملA Threshold-based Similarity Relation Under Incomplete Information
The conventional rough set theory based on complete information systems stems from the observation that objects with the same characteristics are indiscernible according to available information. Although rough sets theory has been applied in many fields, the use of the indiscernibility relation may be too rigid in some real situations. Therefore, several generalizations of the rough set theory...
متن کاملUncertainty Measure of Rough Sets Based on a Knowledge Granulation for Incomplete Information Systems
Rough set theory is a relatively new mathematical tool for computer applications in circumstances characterized by vagueness and uncertainty. In this paper, we address uncertainty of rough sets for incomplete information systems. An axiom definition of knowledge granulation for incomplete information systems is obtained, under which a measure of uncertainty of a rough set is proposed. This meas...
متن کاملTOPOLOGICAL SIMILARITY OF L-RELATIONS
$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...
متن کاملA New Approach for Knowledge Based Systems Reduction using Rough Sets Theory (RESEARCH NOTE)
Problem of knowledge analysis for decision support system is the most difficult task of information systems. This paper presents a new approach based on notions of mathematical theory of Rough Sets to solve this problem. Using these concepts a systematic approach has been developed to reduce the size of decision database and extract reduced rules set from vague and uncertain data. The method ha...
متن کامل