الفهرس 
Contents
Chapter 1Only 14 pages are availabe for public view
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Abstract
To solve complicated problems in economics, engineering, environ-
mental science, medical science and social science, methods in classical
mathematics may not be successfully used because of various uncer-
tainties arising in these problems. Alternatively, mathematical theo-
ries such as probability theory, fuzzy set theory (Zadeh 1965, Zadeh
2005) rough set theory (Pawlak 1982, Pawlak and Skowron 2007),
vague set theory (Gau and Buehrer 1993) and the interval mathemat-
ics (Gorzalczany 1987) were established by researchers to modeling
uncertainties appearing in the above elds.
The concept of soft set was rst introduced by Molodtsov in 1999
as a general mathematical tool for dealing with uncertain objects. In
(Molodtsov (1999), (2001), (2004)) and (Molodtsov et al., (2006)).
Molodtsov successfully applied the soft theory in several directions,
such as smoothness of functions, game theory, operation research, Rie-
mann integration, Perron integration, probability, theory of measure-
ment and so on. Maji et al., (2003) described an application of soft set
theory to a decision-making problem. Pei and Miao (2005)investigated
the relationships between soft sets and information systems. Research
on the soft set theory has been accelerated (see, Feng et al., (2010) and
Zou and Xiao (2008)). This theory has been applied in several direc-
tions such as topology (see, Cagman, and Enginoglu (2010), Cagman
at al., (2011), Min (2011), Shabir and Naz (2011), and Zorlutona et al.,
(2011)). Various algebraic structures (see, Aktas and Cagman (2007),
Feng et al., (2008), Jun (2008) and Jun and Park (2008)), Operations
research (see, Cagman, and Enginoglu (2010), Feng et al., (2012), and
Jiang et al., (2010)). Shabir and Naz (2011) introduced the notion of
soft topological spaceswhich are de ned over an initial universe with
iv
xed set of parameters. They also studied some of basic concepts of
soft topological spaces.
The aim of this thesis is to generalize and extend the basic concepts
in soft topological space, such as soft