In fuzzy systems the two very important key questions, the selection of universe and the description of intentions of concepts, have not been solved within fuzzy sets theory. For solving these questions, the author created the concept of factor space. Define factor space as follow: DEFINITION: A factor space is a set family {X(f)}(f∈F) taking a completed Boolean algebra F = F(∨,∧, c,1,0) as index set, and satisfies the following two items:(2.1)X(0)={φ}(2.2)((AT∈F)(t,s∈T,t≠s)=>s∧t=>0)=>X(∨_t∈TFt0=Ⅱ_t∈TX(Ft) F is called the factor set, f?F is called factor, X(f) is called full space