On Characterizing Hierarchies of Granulation Structures via Distances

Authors:
Xibei Yang;Yuhua Qian;Jingyu Yang
Affiliations:
School of Comp. Sci. and Engineering, Jiangsu University of Sci. and Technology, Zhenjiang, 212003, P.R. China. yangxibei@hotmail.com;Key Lab. of Comp. Intel. and Chinese, Information Processing of Ministry of Education, Taiyuan, 030006, P.R. China. jinchengqyh@126.com;School of Comp. Sci. and Technology, Nanjing University of Sci. and Technology, Nanjing, 210093, P.R. China. yangjy@mail.njust.edu.cn
Venue:
Fundamenta Informaticae
Year:
2013

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Abstract

Hierarchy plays a crucial role in the development of the granular computing. In this paper, three different hierarchies are considered for judging whether a granulation structure is finer or coarser than another one. The first hierarchy is based on the set containment of information granulations, the second hierarchy is based on the cardinal numbers of information granulations while the third hierarchy is based on the sum of cardinal numbers of information granulations. Through introducing set distance and knowledge distance, we investigate the algebraic lattices, in which the derived partial orders are corresponding to the three different hierarchies, respectively. From the viewpoint of distance, these results look forward to provide a more comprehensible perspective for the study of hierarchies on granulation structures.