An approach to finding reduced sets of information features describing discrete objects based on rough sets theory

Abstract

Modern Data Mining methods allow discovering non-trivial dependencies in large information arrays. Since these methods are used for processing and analysis of huge information volumes, reducing the number of features necessary for describing a discrete object is one of the most important problems.One of the classical problems in intelligent data analysis is the problem of classifying new objects based on some a-priori information. This information might not allow us to exactly classify an object as one belonging to a certain set. In such cases using rough sets theory may be an effective solution as this theory operates with the concept of "indiscernible" elements and ambiguous information.In this paper we introduce a concept of a local reduct as a reduced set of features allowing us to describe a particular subset of the original set with the same precision as with the help of the full set of features. A method has been suggested which allows finding reduced sets of features adequately describing a rough set without losing necessary information (so-called reducts), and also assessing the importance of each feature. The suggested method is based on the algebraic approach to finding rough set approximations developed by the authors earlier. The main idea of the developed approach is as follows: if the algebraic approximations of a rough set do not change substantially in the process of excluding features the resulting reduced set of features can be used instead of the original full set. Also the greater changes eliminating a particular feature causes in the approximations, the more important this feature is.

A rough set based algebraic approach to modelling complex systems

“…in our series of papers [2][3][4][5] we try to give the rough set ideology a bit different perspective by avoiding the usage of the knowledge granularity concept. Whereas the classical rough set theory is based on the indiscernibility relation (which can be equivalence, tolerance or other types of relations), we do not use such a notion and try to consider uncertainty from a logic-algebraic viewpoint.…”