Generalized decomposition integral

Choquet-Sugeno-like operator based on relation and conditional aggregation operators

“…A nonempty family H of collections will be called a decomposition system, i.e., H ⊆ 2 Σ 0 \ {∅} (cf. [20]). Several decomposition systems often used in the paper are summarized in the following example.…”

“…Setting F = • in ( 12) we obtain the Pan-integral based on the standard arithmetic operation addition and multiplication [41]. The operator ( 13) is studied in [20] for…”

“…F-decomposition integrals [20] and inclusion-exclusion integral [17]. Obviously there are some functionals belonging to both groups such as seminormed fuzzy integrals [36] and the prominent nonadditive integrals of Choquet [11] and Sugeno [37].…”

“…A detail discussion is included in Examples 3.4-3.9 and in Section 4, where we also give relationships between the existing generalizations of discrete Choquet integral and our Choquet-Sugeno-like operator. As a by-product, we join the works that simultaneously generalize the Sugeno integral and the Choquet integral on finite sets, similarly to the works [20,26,31,39].…”

“…In [8,18,20,23,26,27,28,29,30] the authors study properties of operators ( 1)-( 3) mainly by replacing the product by another binary function. So, it is natural to find a connection between them and the Choquet-Sugeno-like operator.…”