Collection Of Sets Of Areas And Fuzzy Subring (ideal)

This paper consists of two parts.In the first part,a new category called SEB is introduced.First,its topoi properties are investigated.Although category SEB is not a Topos,it is Cartesian Closed.Next,the two subcategories called SSEB1and SSEB2of category SEB are discussed.we discover subcategory SSEB1is a Topos.But subcategory SSEB2is not a Topos,it has middle object and can form a WTopos. In the second part,(β,α)-fuzzy subring is defined.In particular,(∈,∈∨q)-fuzzy subring(ideal)is more important and useful.Definitions of λ L -fuzzy subring(ideal)and λ u -fuzzy subring(ideal)are also introduced.Further on,Concepts of(λ,μ］-fuzzy subring (ideal)and(λ,μ,T S)-fuzzy subring(ideal)are given.Which generalise the above-mensioned fuzzy subrings(ideals).