Choquet integrals, entropy, the Gini index, and applications

Choquet integrals are used for the analysis of annual reports of companies, with a focus on their use of positive words. It is shown that the Choquet integral is able to distinguish one report from another by taking into account of the potential latent relationships of different sections of the annual reports. The robustness of the results in the presence of random noise in the data is discussed. The uniformity of use of positive tone in annual reports is also analysed using entropy and the Gini index. The inverse problem of calculating the capacities from known values of the Choquet integral linked to a certain set of data is also studied (and called ‘training’ of the Choquet integral). These capacities can then be used for the calculation of the Choquet integral for different sets of ‘similar data’. This is exemplified with data related to solar flares.