Covering Based Granular Computing And Its Application

Granular computing is a new computing paradigm, which covers all theories, methods and technologies about granularity. Its key idea is that abservations from multiple views and multiple levels may be done to a real problem and a structured representation of this problem will be gotten. It has been proved that it is an effective method in dealing with complex problems, mining rules from magnanimity information, processing vagueness information, etc. Rough set theory is an important computing paradigm of granular computing, which has been widely used to address the problems with imprecision, incompleteness and vagueness.The classical rough set theory is based on an equivalence relation on a universe which is a representation of knowledge in a granularity. Becase it is not impossible or cost too much to get an equivalence relation on a universe, it is limited in practical use. Hence, many interesting extended rough set models have been studied in the past yesrs. Particularly, covering generalized rough set model uses coverings as the representation of knowledge, and it has the characteristic of not relying on repsentation of information.In this paper, we use rough set theoy as the computing method, covering as the repsentation of knowledge, and try to construct a covering based granular computing model. Some results listed as follows have been gotten on several key problems in covering based granular computing model, such as uncertainty measure of covering generalized rough set, fuzzy concept approximation in covering approximation space, knowledge reduction of covering approximation space, extension of covering approximation space and its application, etc.(1) A modified fuzziness of covering generalized rough set is proposed, and it corrects the unreasonability in existing uncertainty measures.For Bonikowski's covering generalized rough set, some existing uncertainty measures have been analyzed, and their limitation are illustrated by some examples. Based on the hypothisis that roughness and fuzziness are equal in characterizing uncertainty, a mapping between rough sets and fuzzy sets is constructed by a rough belongingness fuction, and then a modified fuzziness of covering generalized rough sets is developed. This new fuzziness overcomes the limations of the existing uncertainty measures, and it is in line with the cognitive characteristics of human. (5) Through extending each covering induced by every attribute in a covering decision system, a heuristic attribute reduction algorithm is proposed. The theoretic analysis and simulation results indicate that this algorithm can get more concise reduction than existing algorithms.By defining the complement of a covering, the complement space and extended space are proposed. It is proved that the original space, complement space and extended space are equal in knowledge when the covering degenerated into a partition. However, this result is not held in generally, and the extended space is more precise in knowledge than the original space. Through extending covering approximation spaces induced by each attribute, a heuristic atttirbute reduction algorithm is developed. The theoretics analyse and practical running prove that this algorithm can get less attribute number than other methods.