Discrete IV d-Choquet integrals with respect to admissible orders

In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021 This work was supported in part by the Spanish Ministry of Science and Technology, under project PID2019-108392GB-I00 (AEI/10.13039/501100011033), by the project PJUPNA-1926 of the Public University of Navarre and by the project VEGA 1/0267/21 .