In this work we discuss the forms of monotonicity that have been recently introduced to relax the monotonicity condition in the definition of aggregation functions. We focus on directional, ordered directional and strengthened ...

In this work, we propose a new notion of monotonicity: strengthened ordered directional monotonicity. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent ...

A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss ...

In this work we propose a generalization of the notion of directional monotonicity. Instead of considering increasingness or decreasingness along rays, we allow more general paths defined by curves in the n-dimensional ...

In this work we consider some classes of functions with relaxed monotonicity conditions generalizing some other given classes of fusion functions. In particular, directionally increasing aggregation functions (called also ...

In the theory of aggregation, there is a trend towards the relaxation of the axiom of monotonicity and also towards the extension of the definition to other domains besides real numbers. In this work, we join both approaches ...

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the 'standard' Choquet integral obtained by replacing the difference in the definition ...

We consider mixture functions, which are a type of weighted averages for which the corresponding weights are calculated by means of appropriate continuous functions of their inputs. In general, these mixture function need ...