Adapted integral representations by measures on Choquet boundaries

Adapted Integral Representations by Measures on Choquet Boundaries

On the Choquet integral for Riesz space valued measures

The Choquet integral is defined for a real function with respect to a fuzzy measure taking values in a complete Riesz space. As applications there are presented: constructions of belief and plausibility measures, the formulation of an extension principle, and the Möbius transform for vector values measures.

Fuzzy Measures and Choquet Integral on Discrete Spaces

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

Modelling data by the Choquet integral

It is well known that the main tool for finding dependencies among data is the linear regression model, which expresses one or several variables in term of a linear combination of the others. Linear regression is based on the least square principle, and has been studied at length, its statistical performance are well known. In real situations however, the linear assumption happens to be often r...

Choquet Integral Based Evaluations by Fuzzy Rules

Choquet-integral-based evaluation models are proposed. The evaluation parameters – fuzzy measures – are assigned from a fuzzy rule table. There are three variations in this model: TF-, BP-, and AV-type models. The TF-type model is a natural extension of ordinal Choquet integrals. The BP-type model involves an evaluation using a reference point. The AV-type model involves a neutral evaluation me...