Bicapacities  Part II: the Choquet integral
Abstract
Bicapacities 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 bicapacities, 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 Möbius transform. This permits to express the Choquet integral for 2additive bicapacities w.r.t. the interaction index.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2112
 Bibcode:
 2007arXiv0711.2112G
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Computer Science and Game Theory
 EPrint:
 Fuzzy Sets and Systems (2005) 237259