Sufficient and ε-sufficient statistics in pattern recognition and their relation to fuzzy techniques

An approach to the selection of essential features of objects to be recognized, which is based on sufficient and ε-sufficient statistics, is presented. It is shown how sufficient and ε-sufficient statistics can be used to construct partitions of the space of outcomes of an experiment in order to simplify the pattern recognition process. Whereas the sufficient partitions involve inexactness represented by exact statistical information, the use of ε-sufficient partitions simplifies the decision-making process but at the same time introduces additional inexactness or fuzziness. The relation of ε-sufficient data reduction to fuzzy techniques is shown by defining the grade of membership and the degree of fuzziness in terms of the model introduced