  Notions of core, support and inversion of a soft set have been defined and
studied. Soft approximations are soft sets developed through core and support,
and are used for granulating the soft space. Membership structure of a soft set
has been probed in and many interesting properties presented. The mathematical
apparatus developed so far in this paper yields a detailed analysis of two
works viz. [N. Cagman, S. Enginoglu, Soft set theory and uni-int decision
making, European Jr. of Operational Research (article in press, available
online 12 May 2010)] and [N. Cagman, S. Enginoglu, Soft matrix theory and its
decision making, Computers and Mathematics with Applications 59 (2010) 3308 -
3314.]. We prove (Theorem 8.1) that uni-int method of Cagman is equivalent to a
core-support expression which is computationally far less expansive than
uni-int. This also highlights some shortcomings in Cagman's uni-int method and
thus motivates us to improve the method. We first suggest an improvement in
uni-int method and then present a new conjecture to solve the optimum choice
problem given by Cagman and Enginoglu. Our Example 8.6 presents a case where
the optimum choice is intuitively clear yet both uni-int methods (Cagman's and
our improved one) give wrong answer but the new conjecture solves the problem
correctly.
