Partial Lattice-Valued Possibilistic Measures and Some Relations Induced by Them

Abstract

For a number of reasons rooted in our surrounding real world, the degrees of uncertainty and, in particular, the values of possibilistic measures related to various phenomena, need not be definable quantitatively, by real numbers from the unit interval, say, but rather only qualitatively and related to each other (greater than, not smaller than,...). Moreover, the values of possibilistic measures need not be known or even defined for every event from the field of events under consideration. Three extensions of partial lattice-valued possibilistic and necessity measures to the whole system of events under consideration are introduced and some assertions showing their various properties and mutual relations are presented and proved.