D.A.Molodtsov (1999), started with the soft set theory as a mathematical tool to deal with problems in which there is some suspicion which the usual mathematical tools are unable to resolve , because of the necessity of finding new solutions for these problems , this scientist has put many tools to resolve some of problems that are in concern with human life directly or un directly .
In [D.A.Molodtsov (1999), P. Majumder and S . K .Samanta , (2012), I . Zorlutuna , M . Akdag , W.K Minand S. Atmaca (2012), N . Cagman ,F . Cltak and S . Enginolu (2001), N.Cagman and S .S . Englinglu (2011), P. Majumder and S . K .Samanta (2012), P.k.Maji , R.Biswas and A.R.Roy (2003), P.k.Maji , and A.R.Roy (2002), S.M.Modumugal pal (2013)] , the fact that we must focus on is that all of these researches depending on the following fact when defining the soft set :
If ? is a universal set and A be a subset of a set of parameters E , then a soft set F_A,F:A?IP(?) is not the null soft set , ( I . e F_A?? ?_A ? a?A if and only if F(a)?? ? a?A , where ? ?_A is the null soft set [F(a)=? ? a?A] .
We will proof in the following papers that this condition need not be true , but it is special case for the following condition :
If F_A is not the null soft set a?A such that F(a)?? .
This means that it is sufficient for existing only one element whose image is not the null soft set . in such case the soft set will not be null soft set and we will explain that in an example.
One of the agreed upon facts which concern the origin of the soft set is that the dynamicity by which these types of sets have been invented in the following way :
F_A={(a,F(a)),a?A ,F(a)?IP(?)} and ?a?A , then (a,F(a)) ?F_A .
Many of the researches studies where o the family points which is the result of the cross between the two coordinates of the two soft sets
( I . e {a}×F(a)={(a,x),x?F(a)}?A×?.
From above we can conclude that each of the ordered pairs may be dealt whit individually as (soft set) if we considered the set F(a)={x}when the study is on the point a?A ,so?
(x,a) is an a-soft point if and only if {(a,x)}?{a}×F(a) is a soft set .
All these notes be explained more in the following papers .
In [P.k.Maji , R.Biswas and A.R.Roy (2003)] the example (2.6) is incorrect in that we believe the soft set G_B , does not necessary represent a soft set according to the definition introducing by molodtsov [D.A.Molodtsov (1999)] , because the fact that be in mind is that the set ?A is a subset of the set of all Parameters E_? , if it is so , it is possible to be a domain of the relation F , and F_A will be a soft set . in fact the set ?A , is an ambiguous set (whose feature are not clear) from the set E_?; because E_? is also ambiguous . As we mentioned that they might be signs , features , or symbol , and the signs and the feature are facts that cannot be restricted . and excluding element of a subset from E_? does not mean that the remaining is always excluding (A) elements. In other word we can’t from which the rest of the unknown number parameters that represent ?A , consequently , this expression will not be accurate at all.