Methodology of rough-set-based classification and sorting with hierarchical structure of attributes and criteria

We consider a hierarchical classification problem involving sets of attributes and criteria. The problem of classification concerns an assignment of a set of objects to pre-defined classes. The classification to preference-ordered classes is called sorting. The objects are described by two sorts of attributes: criteria and regular attributes, depending on whether the attribute domain is preference-ordered or not. The hierarchical classification and sorting is made in finite number of steps due to hierarchical structure of regular attributes and criteria in the form of a tree. We propose a methodology based on the decision rule preference model. The model is constructed by inductive learning from examples of hierarchical decisions made by the Decision Maker on a reference set of objects. To deal with inconsistencies appearing in decision examples we adapt the rough set approach to the hierarchical classification and sorting problems. Due to inconsistency and their propagation from the bottom to the top of the hierarchy, the description of an object on a particular attribute may be not a simple value but either a subset of a regular attribute domain or an interval on a criterion scale. An example illustrates the methodology presented.