Abstract:

In order to further study DFIalgebra, firstly, the definition of a distance function in DFIalgebra was given. Its properties were discussed, and some special properties of the distance function of some kinds of special DFIalgebras, for example, linear DFIalgebras were given. Secondly, a new operation was introduced in DFIalgebra, and the equivalent definition of the distance function of DFIalgebras and some farther properties were given; finally, the corresponding metric space based on the distance function was introduced.

Key words: FIalgebra, regular FIalgebra, DFIalgebra, distance function