Fuzzification operator for rough sets in image segmentation

Recent advances in computer science and information systems design have shifted the requirement into the domain of the intelligent information systems. In the last decades, many new data analysis tools and methodologies have been devised in order to keep abreast with the massive increase in data amount and types. Rough Extended Framework has been recently introduced in the domain of employing rough sets based data analysis in the unified framework of fuzzy and statistical analysis. Much effort in the area of REF Framework is focused on the data structure exploration by the means of examining of metric dependencies between analyzed data and the reference set, most often composed of certain number of clusters or thresholds that are selected objects of the input data space. In the paper, in the Rough Extended (Entropy) Framework, a new generalization of the concept of RECA sets has been presented by means of fuzzification of the RECA sets. The introduced solution seems to present highly robust and detailed theoretical and mathematical tool during examining internal data structure. © 2011 Springer-Verlag Berlin Heidelberg.