Bi-capacities -- Part II: the Choquet integral

Details Bi-capacities -- Part II: the Choquet integral Bi-capacities -- Part II: the Choquet integral

2007-11-14

arxiv.org/abs/0711.2112v1

Fuzzy Sets and Systems (2005) 237-259

Computer Science

Discrete Mathematics

Scientific paper

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.

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