Multi-polar Choquet integral

The choice of a bipolar scale in decision making relates to an ideal situation where positive and negative evaluations reflect a decision maker's choice on a binary scale. However, decision making space is essentially an interval comprising extended scales, e.g., three point scale where there can be decisions about gains, losses and a neutral stance by the decision maker for not risking anything. Work in affect analysis shows that textual information can serve as one source for estimation of risk related with stock investment. Based on aggregation of several components of text belonging to different categories the overall category of textual information can be obtained and related to a risk position at any given time point. We explore the notion of multi-polarity in decision making by extending the notion of bipolar Choquet integrals to multi-polar Choquet integrals. We introduce extensions of basic bipolar Choquet integrals, the balancing Choquet integral and the Choquet integral with respect to a bi-capacity.