Aggregation function; Choquet integral; cognitive integral; decision making; preaggregation function; Shilkret integral; Sugeno integral; universal integral

Motivated by some cognition styles, this study first proposes a new type of preaggregation functions called cognitive integrals with its generalized forms. Rather than being affected only by selected capacity, generalized cognitive integrals consider other two parameters, the cognitive strength and the involved semi-copula. Our main focus is on cognitive strength, by which the integrals values will he monotonically decreasing with respect to our cognitive strength. After some appropriated adaptations, we later propose the concept of adapted cognitive integrals with two equivalent forms of itself. Not only being a type of the preaggregation functions, we prove that adapted cognitive integrals are indeed one new type of aggregation functions, still equipped with the two new parameters like in cognitive integrals.