The Interval-Valued Choquet Integral Based on Admissible Permutations

Aggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, we propose the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.