Recent research has highlighted the importance of studying the different forms of monotonicity for various discrete Choquet-like integrals in the field of data aggregation and its real-world applications. In this paper, we focus on the standard monotonicity condition for two operators encompassing many modifications of the discrete Choquet-like integral known in the literature, such as the CQO-integral, the C T -integral, the CC-integral, the CO-integral, or the n -ary discrete d -Choquet integral. Using a new approach, we provide complete monotonicity characterizations for both operators. This, in turn, allows us to give full characterizations of the operators as aggregation functions. Our results extend and complete some results in the literature.

A monotonicity of Interval Sugeno Integrals proposed in “X. Pu, R. Mesiar, R. R. Yager, L. Jin, Interval Sugeno integral with preference,” IEEE Trans. Fuzzy Syst. vol. 28, pp. 597-601, 2020 has been found incorrect with a counter example. This letter presents the counter example and analyzes the reason that causes such nonmonotonicity. In addition, two new related forms of Interval Sugeno Integrals are also proposed, which feature the synchronizations about values and subsets, respectively. The similar monotonicities for the new forms are proved to be correct.