For studying structures of granular spaces, we have given a uniform knowledge representation method for various types of granular spaces, and have presented intersection, union, complement and difference operators, which can be used to composition, decomposition and transformation operations among crisp/fuzzy granular spaces。 It can be proved that all granular spaces from a universe and these four operators can form a complete complemented lattice, which reveals the hierarchical structure property of granular spaces from algebra viewpoint。 In addition, we have also proposed a knowledge distance and a fuzzy knowledge distance, the knowledge/fuzzy knowledge distance and the crisp/fuzzy granular spaces founds a distance space, which reveals the geometry structure property of granular spaces from the geometry viewpoint。 

For information granulation, we have given several information granularity measures for the crisp granular space and the fuzzy granular space, and have established the corresponding axiomatic approach to the crisp/fuzzy information granularity respectively。 These results uniform relative measures of information granularity in the context of various types of granular spaces and reveal the essence of crisp/fuzzy information granularity measure, which provide constrained theory and directable method for studying granulation uncertainty。

3。 Through referencing human’s granulation cognitive ability, we have developed three kinds of modeling methods based on multigranulation, dynamic granulation and ordered granulation, respectively, which largely promoted the development of data modeling based on granulation mechanism。

Through referencing human’s multigranulation cognitive ability, we have established three kinds of multigranulation modeling methods, which are based on ‘Seeking common ground while reserving differences’(SCRD), strategy ‘Seeking common ground while eliminating differences’(SCED) strategy and ‘Concept description’ strategy respectively, which largely enrich modeling theories and methods based on rough set theory。 The proposed multigranulation rough sets can be widely applied data analysis under multigranulation contexts, such as distributive information systems and groups of intelligent agents。

Through referencing human’s dynamic granulation cognitive ability，we have given methods to concept approach and decision approach under dynamic granulation, and have proposed a general accelerator for rough feature selection，which provides an efficient strategy for heuristic feature selection in rough set theory。 From theoretical analysis and experimental results, one can draw conclusions:

(a) each of the accelerated algorithms preserves the attribute reduct induced by the corresponding original one; 

(b) each of the accelerated algorithms usually comes with a substantially reduced computing time when compared with amount of time used by the corresponding original algorithm; 

(c) the performance of these modified algorithms is getting better in presence of larger data sets; the larger the data set, the more profound computing savings。 Furthermore, we have also developed a structure dimensionality reduction strategy combining feature reduction and sample reduction together, and have designed a very efficient algorithm for rule extraction based on this strategy。 Experimental results show that both computational time and decision performance are much better than each of existing methods, which will provide an efficient method for knowledge discovery from large-scale data sets。

 Through referencing human’s ordered granulation cognitive ability, we have given semantic description of each of interval data, conjunctive set-valued data and disjunctive set-valued data, have established rank decision and grading decision based on ordered granulation, and have proposed a feature selection method based on rank-preservation, which can effectively select a feature subset from an ordered information system and an ordered decision information system。 These results further perfect the theories and methods of rank decision and grading decision, and also provide new viewpoints for ordered classification and ordered clustering, and others。