文档介绍：Chapter 24
PUTING AND ROUGH SETS
An Incremental Development
Tsau Young ('T. Y.') Lin
DepaHment puter Science
San Jose State University
San Jose, CA 95192
tylin
Churn-Jung Liau
Institute of lnfonnation Science
Academia Sinica, Taipei 115, Taiwan
Abstract This chapter gives an overview and refinement of recent works on binary granu-
puting. parison and contrasting, granulation and partition are ex-
amined in parallel from the prospect of rough Set theory (RST).The key strength
of RST is its capability in representing and processing knowledge in table for-
mats. Even though such capabilities, for general granulation, are not available,
this chapter illustrates and refines some such capability for binary granulation.
In rough set theory, quotient sets, table representations, and concept hierarchy
trees are all set theoretical, while in binary granulation, they are special kind
of pretopological spaces, which is equivalent to a binary relation Here a pre-
topological space means a space that is equipped with a neighborhood system
(NS). A NS is similar to the classical NS of a topological space, but without any
axioms attached to it1.
Keywords: puting, rough set, binary relation, equivalence relation
1 Introduction
Though the label, puting is relatively recent, the notion of
granulation has in fact been appeared, under different names, in many related
536 DATA MINING AND KNOWLEDGE DISCOVERY HANDBOOK
fields, such as programming, divide and conquer, fuzzy and rough set theo-
ries, pretopological spaces, puting, quantization, pres-
sion, chunking, cluster analysis, belief functions, machine learning, databases,
and many others. In the past few years, we have seen a renewed and fast
growing interest in puting (GrC). Many applications of granular
computing have appeared in fields, such as medicine, economics, finance, busi-
ness, environment, electrical puter