Lattice-Valued Possibilistic Entropy Functions

Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete lattice is completely distributive in the defined sense, the entropy values defined by independent products of finite sequences of lattice-valued possibilistic distributions are proved to be defined by the supremum value of the entropies defined by particular distributions.