Unifying Rough Set Theories via Large Scaled Granular Computing

Authors:
Tsau Young Lin;Yong Liu;Wenliang Huang
Affiliations:
Department of Computer Science, San José State University, San José, CA 95192, USA. tylin@cs.sjsu.edu;Institute of Cyber-Systems and Control, Zhejiang University, Hanghzou, 310027, PR China. yongliu@iipc.zju.edu;China United Network Communication Corporation, 100032 Beijing, China. huangwl0901@gmail.com
Venue:
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
Year:
2013

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Abstract

This paper explains the mathematics of large scaled granular computing GrC, augmented with a new Knowledge theory, by unifying rough set theories RS into one single concept, namely, neighborhood systems NS. NS was first introduced in 1989 by T. Y. Lin to capture the concepts of “near” topology and “conflict” security. Since 1996 when the term Granular Computing GrC was coined by T. Y. Lin to label Zadeh's vision, NS has been pushed into the “heart” of GrC. In 2011, LNS, the largest NS, was axiomatized; it implied that this set of axioms defines a new mathematics that realizes Zadeh's vision. The main messages are: this new mathematics is powerful and practical.