Discrete bipolar pseudo-integrals

In the authors paper (Štrboja et al., 2016) [42], the notion of the bipolar pseudo-integral has been introduced. This paper extends investigations related to this new type of bipolar integrals defined with respect to ⊕-decomposable bi-capacities. We consider the main properties of the discrete bipolar pseudo-integral. A characterization theorem for the discrete bipolar pseudo-integral is proven. Monotone convergence theorems and the Fatou type lemma for the discrete bipolar pseudo-integral are considered. In order to illustrate obtained results, many interesting examples are provided.