On the extension of P-consistent mappings
L Boyen, Gert de Cooman, Etienne E. Kerre · 1995
In this paper, the notion of P-consistency is extended to complete lattice-valued mappings. It is proven that a P-consistent mapping possesses a distribution if and only if it is extendable to a possibility measure defined on an ample field. A necessary and sufficient condition is given for extendability, and it is shown by counterexamples that this condition is not always satisfied. Finally, sufficient conditions are given under which a P-consistent mapping is always extendable, and it is shown that every complete lattice can be embedded in another complete lattice in such a way that every P-consistent mapping is extendable to a possibility measure taking values in the second complete lattice. 1. Introduction Ever since the introduction of possibility theory by Zadeh 8 in 1978, various attempts have been made to generalize Zadeh's original definition of a possibility measure. Essentially, Zadeh defined a possibility measure \\Pi as a mapping from the power class (X) of a non-empty s...