| This thesis deals with the subalgebras of algebras of truth values of type-2 fuzzy sets over non-distributive lattices.It first constructs a subset of functions between a bounded lattice and a frame,and then proves that the subset together with the convolution operation is a bounded distributive lattice.It also constructs a Birkhoff system of functions between a bounded lattice and distributive lattice and a frame.This partly answers the open problem posed by L.De Miguel,H.Bustince and B.De Baets in their paper"Convolution lattices"[Fuzzy Sets and Systems 2018,335:67-93].Based on these,we give some concrete examples and try to find other ways to construct bounded distributive lattices. |
