(eng): In many real-world cases, disjunction is expressed as the fusion of full alternatives and less relevant ones, which leads to an OR ELSE connective. Obviously, this connective, so-called intensified disjunction, should provide a solution lower than or equal to the MAX operator, and higher than or equal to the projection of the full alternative. Further, to cover the cases when higher satisfaction degrees to the less relevant alternative cause that it becomes the full alternative, non–continuous asymmetric disjunction is required. The dual observation holds for the fusion of constraints (hard conditions) and wishes (soft conditions) expressed by an AND IF POSSIBLE connective. In order to cover these requirements, the paper focuses on developing a full axiomatization of asymmetric disjunction and asymmetric conjunction by averaging functions. Next, the necessity and sufficiency for associative behaviour have been proven. Moreover, the non-dual cases are also documented. Finally, the obtained results are illustrated on examples, and their applicability is also discussed.