Information Technology Reference
In-Depth Information
Chapter 11
Rough Set
11.1 Introduction
In classical logic, there are only two values: true and false. However, in reality,
some ambiguous phenomena can not be briefly represented by true and false.
Thus, how to describe and deal with these phenomena becomes a research topic.
A lot of logicians and philosophers have been devoted to studying the vague
concept for a long time. Since 1904, the founder of predication logic G. Frege
proposed the word—Vague. He considered the concept on the boundary line.
That is to say, some individuals in universe can be classified neither into a subset
nor into the supplementary of the subset.
The term “fuzzy set” was proposed by Zadeh in 1965, which was later used
by computer scientists and logicians in attempt to explain Frege's definition of
“vague”. However, fuzzy set is incomputable, that is, there is neither mathematic
formula to describe this ambiguous concept nor practical approach to calculate
the exact number of its vague elements, such as the membership function
Ⱥ
in
fuzzy sets and the operator
ȹ
in fuzzy logics. Twenty years later, in early 80s,
according to Frege's idea of boundary region, Rough Set was first proposed by
Pawlak in Poland (Pawlak, 1982). He concluded that individual elements that
can't be determined should be incorporated into the boundary region which is
defined as the difference of the upper approximate set and the lower approximate
set.
Based on its concrete description of mathematic formula, the number of
vague elements is computable, which in terms makes the degree of vagueness
between the values of true and false computable. Rough set theory provides an
ordinary rough set approach for processing ambiguous problems, that is, the
ability to handle uncertainty based on incomplete information or knowledge as
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