Discrete IV dG-Choquet integrals with respect to admissible orders

Abstract In this work, we introduce the notion of d G -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 d G -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 d G -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.