  Bi-capacities arise as a natural generalization of capacities (or fuzzy
measures) in a context of decision making where underlying scales are bipolar.
They are able to capture a wide variety of decision behaviours, encompassing
models such as Cumulative Prospect Theory (CPT). The aim of this paper in two
parts is to present the machinery behind bi-capacities, and thus remains on a
rather theoretical level, although some parts are firmly rooted in decision
theory, notably cooperative game theory. The present second part focuses on the
definition of Choquet integral. We give several expressions of it, including an
expression w.r.t. the M\"obius transform. This permits to express the Choquet
integral for 2-additive bi-capacities w.r.t. the interaction index.
