On a Particular Class of Lattice-valued Possibilistic Distributions

Investigated are possibilistic distributions taking as their values sequences from the infinite Cartesian product of identical copies of a fixed finite subset of the unit interval of real numbers. Uniform and lexicographic partial orderings on the space of these sequences are defined and the related complete lattices introduced. Lattice-valued entropy function is defined in the common pattern for both the orderings, naturally leading to different entropy values for the particular ordering applied in the case under consideration. The mappings on possibilistic distributions with uniform partial ordering under which the corresponding entropy values are conserved as well as approximations of possibilistic distributions with respect to this entropy function are also investigated.