The classification of preordered spaces in terms of monotones: complexity and optimization

The study of complexity and optimization in decision theory involves both partial complete characterizations preferences over spaces terms real-valued monotones. With this motivation, following the recent introduction new classes monotones, like injective monotones or strict monotone multi-utilities, we present classification preordered existence cardinality quotient space. In particular, take advantage a characterization separating families increasing sets order to obtain more consisting that are strictly different from each other. As result, gain insight into optimization, clarify their interplay spaces.