The Research On Multigranulation Rough Computing Theory And Approach

With the rapid development of information technology, especially the wide application of modern network and cloud computing technology, data volume and data sources increases and the relevant hierarchies are also becoming more and more complex. In the modern society, complicated large data with characteristics of multiple sources and multiple modes has become the main body data resources and knowledge discovery. So the traditional data processing technology encounters the great challenges.As an important tool for knowledge acquisition and problem solving, granular computing uses information granules instead of samples in the process of problem solving. It often analyses problem from multiple views and multiple hierarchies, which can obtain more reasonable and more satisfied solution for the problem. This paper carries out a detailed and systematic research on the multigranulation rough computing theory and approach, which will provide a new approach for information fusion on the multi-source information and enrich the applicable fields. The main research findings are summarized as follows:(1) We give the representation of the information granulation struc-ture and a fusion model for the multi-source symbolic data and fuzzy data. To generalize the modeling ability and the applicable range of the clas-sic multigranulation rough set, we first propose three kinds of optimistic and pessimistic covering-based multigranulation rough sets and then re-veal some properties and the difference among them. Thus, these results will provide the theoretical basis for rough data analysis of the multiple sources data and provide effective guidance for the selection of the rough set model in the context of multiple sources.(2) From the topological view, we investigate a new theory on multi-granulation rough sets. Multigranulation topological rough space and its topological properties are explored by introducing new definitions and theorems. In addition, according to the invariance of the interior and the closure, a granulation space selection algorithm is given and the effective-ness of the proposed algorithm is illustrated by an example.(3) We present three uncertainty measures for multigranulation s-pace from the different views. Firstly, fusion information entropy, fu-sion knowledge fusion and fusion rough entropy are introduced based on the fusion approach of the information uncertainty measurement. Sec-ondly, the topology entropy and topology granulation are given for the multigranulation topology space. Then, roughness and rough entropy for covering-based multigranulation rough sets are proposed. At last, we have discussed some of their important properties. These results will be help-ful for understanding the nature of the uncertainty in multigranulation computing theory.(4) Based on the evidence theory, we have proposed a new multi-granulation fusion algorithm. We have addressed the connection between the classical/fuzzy multigranulation rough set theory and the classica-ble/fuzzy evidence theory. Then, we have proposed a two-grade fusion approach involved in the evidence theory and multigranulation rough set theory, which is based on a well-defined distance function among gran-ulation structures. The results of this study will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing.(5) According to the disadvantage of the existing evaluation mea-sures of rule performance, we give the whole certainty measure, the whole consistency measure, and the whole support measure. The theoretical analysis and the experimental results have shown that the three proposed evaluation measures are all better than the approximation precision and the approximation quality.This research results of this paper attain significant fruits on multi-granulation rough calculation theory and approach:proposing covering-based multigranulaiton rough sets for multi-source data; establishing some uncertain measurements for the multigranulation topology space and multi-granulation approximation space; addressing the relationship between the multigranulation qualitative fusion operator and quantitative belief func-tion of evidence theory; proposing a multiple granulation fusion algorithm based on evidence theory; and exploring the performance evaluation of the overall decision fusion method. These findings enrich the multigranulation rough calculation theory and method and provide a theoretical guidance and technical support in the process of handling the complex multi-source data.