Information Technology Reference
In-Depth Information
does not include the mechanism to handle raw data that is inaccurate or
uncertain. Thus, it does not guarantee to give an effective description of
inaccurate or uncertain practical problems, and supplementary methods are
required. Generally speaking, evidence theory and fuzzy set theory are natural
complements of rough set theory because they provide alternative approaches to
handle inaccurate and uncertain data (though it is somewhat difficult to describe).
In order to have a better understanding of the essence and characteristics of
rough set theory, basic definitions are introduced here to explain the essential
idea of rough set theory and its difference compared to other mathematics tools
in handling uncertainty and fuzziness.
11.1.1
Categorized View of Knowledge
Basic rough set theory concludes that knowledge is the ability of human and
other species to distinguish and categorize. For example, in real world knowledge
about environments mainly refers to a creature's ability to distinguish different
situations according to its sense of existence. Every creature forms a complex
classification mode according to its sensor signals, that is, its basic mechanism.
Classification is the crucial problem of inference, learning, and decision making.
Thus, rough set theory assumes that knowledge is the ability to classify specific
objects. Here the term “Object” refers to almost anything we can think of, such as
matter, status, abstract concept, process, and time point, etc. Moreover,
knowledge must be related to the classification modes of specific parts of the
concrete or abstract world. This specific part is called the universe of discussion.
There is no special assumption about the characteristics of the universe and
knowledge. In fact, knowledge constitutes a family of classification modes in a
specific area of interests which provides dominant facts about the reality and the
ability to deduct recessive facts based on these dominant facts.
For mathematical convenience, equivalent relation is used to replace
classification in the following definition.
Definition 11.1
A approximate space is defined as a relationship system
K=(U,
R
),
(11.1)
where U, called as universe, is the set of all discussed objects, and
R
is a family
set of equivalence relation on U.
