Fuzzy Areas, Fuzzy Topology And Related Issues

In this thesis,some work was done on fuzzy category and fuzzy topology. We introduced the concept of the fuzzy subobject in a topos,established category FC formed by fuzzy subobjects in a topos C,and proved FC is finite and complete.In the study on fuzzy topology, the concept of (α,β)-fuzzy topology was given,furthermore ,λ-fuzzy topology was introduced.We explored the relation of weight and intuitionistic fuzzy set, obstained the concept of lattic order relation and lattic pre-order relation, which developed the concept of order-homomorphism and discussed the problem of the rise of pre-order.