Every invariant biseparable preference relation can be represented by an integral on the set of continous a¢ ne mappings over a set of priors, where the integral is taken in the sense of Choquet. In looser terms: the representation takes the form of an integration over priors. As a by-product, we provide a novel interpretation of the (f)-MEU functional and of its relation with the Choquet integ...

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of intervalvalued functions. We also discuss convergence in the C mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem f...

Recent developments in the theory of choice under uncertainty and risk yield a pessimistic decision theory that replaces the classical expected utility criterion with a Choquet expectation that accentuates the likelihood of the least favorable outcomes. A parallel theory has recently emerged in the literature on risk assessment. It is shown that a general form of pessimistic portfolio optimizat...

The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete intervalvalued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet i...

In this paper we studied two different classifiers fusion algorithms exploiting the combination weights expressed over the entire data space and the combination with data dependent weights. The following aggregation schemes are employed in the study: the majority vote, the averaging, the combination via Choquet integral with the − λ fuzzy measure, the combination via space partitioning and clas...

This paper proposes a generation method of facial expressions using fuzzy measure and fuzzy integral for robotic heads. Human’s emotion state can be represented by a fuzzy measure which can effectively deal with ambiguity. Because facial expressions are usually ambiguous such that it is difficult to discern emotions and assign a sharp boundary to each emotion. In this method, users can adjust t...