Abstract:
Let X be a set, L a Hutton algebra, FT(X,L), FN(X,L), FI(X,L) and FC(X,L) denote the set of all L-fuzzy topologies on X, the set of all L-fuzzy neighborhood operators, the set of all L-fuzzy interior operators, and the set of all L-fuzzy closure operators,respectively. The paper gives a one-to-one correspondence φ32 (resp., φ34) from FI(X,L) to FN(X,L) (resp., to FC(X,L)) and a one-to-one correspondence φ24 from FN(X,L) to FC(X,L).It is proved that an appropriate order relation can be defined on FT(X,L) (resp., FN(X,L), FI(X,L), FC(X,L)) such that φ32, φ34 and φ24 are all complete lattice isomorphisms.
