Cassifctinof Objects by-Means of Features

The problem considered in this paper is how to classify objects by means of features. The solution to this problem stems from the seminal work by Zdzislaw Pawlak starting in the early 1980s, which led to the discovery of rough sets and approximation spaces. The interpretation of features in this paper takes its inspiration from the Pawlak´s approach to knowledge representation systems. Explicit in the original work of Pawlak is a distinction between attributes of objects and knowledge about objects. In this paper, knowledge about an object is represented by a measurement associated with a feature of an object. In general, a feature is an invariant characteristic of objects belonging to a class (e.g., select contour (outline) as a feature, where all objects in a class have an identifiable contour). Associated with each feature is a set of probe functions, where each probe function maps objects to a value set. The distinction between features and corresponding probe function values is usually made in the study of pattern recognition. Examples of approximations, approximation spaces and a granular approach to recognition of patterns in pairs of images, are given. The contribution of this paper is a straightforward refinement of Pawlak´s original approach to classifying objects