الفهرس 
Approval Sheet
Pawlak approximation spacesOnly 14 pages are availabe for public view
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Abstract
The volume and complexity of the collected data in our modern society is growing rapidly. There often exist various types
of uncertainties in those data related to complex problems in
biology, economics, ecology, engineering, environmental science,
medical science, social science, and many other fields. In order to describe and extract the useful information hidden in
uncertain data, researchers in mathematics, computer science
and related areas have proposed a number of theories such as
probability theory, fuzzy set theory [26], rough set theory [20],
vague set theory and interval mathematics. Fuzzy set theory appeared for the first time in 1965, in famous paper by Zadeh [26].
Since then a lot of fuzzy mathematics have been developed and
applied to uncertainty reasoning. In this theory, concepts like
fuzzy set, fuzzy subset, and fuzzy equality (between two fuzzy
sets) are usually depend on the concept of numerical grades of
membership. On the other hand, rough set theory, introduced
by Pawlak in 1982 [20], is a mathematical tool that supports also
the uncertainty reasoning but qualitatively. Their relationships
have been studied. While all these theories are well-known and
often useful approaches to describing uncertainty, each of these
theories has its inherent difficulties as pointed out by Molodtsov
[17]. The reason for these difficulties is, possibly, the inadequacy of the parametrization tool of the theories. Consequently,
Molodtsov initiated the concept of soft theory as a mathematical tool for dealing with uncertainties which is free from the
above difficulties. Soft set theory has a rich potential for applications in several directions, few of which had been shown
by Molodtsov in his pioneer work [17], a wide range of applications of soft sets have been developed in many different fields,
including the smoothness of functions, game theory, operations
research, Riemann integration, Perron integration, probability
theory and measurement theory. There has been a rapid growth
of interest in soft set theory and its applications in recent years.