Directional and Ordered Directional Monotonicity of Generalized and Bounded Generalized Mixture Functions

Generalized Mixture (GM) and Bounded Generalized Mixture (BGM) functions, as well as OWA and Choquet integrals, are weighted averaging functions which provide a broad class of fusion functions. However, both, OWA and Choquet Integrals, satisfy the monotonicity condition, which fails for some GM and BGM functions. In this paper we investigate two generalized forms of monotonicity: The directional monotonicity and ordered directional monotonicity, then we determine some criteria for obtaining GM and BGM functions which satisfy such properties.