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Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Theory and Decision [ISSN:] 1573-7187 [Volume:] 94 [Issue:] 4 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 693-720
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued monotones in terms of separating families of increasing sets to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces.
Schlagwörter: 
Multi-utility representation
Richter–Peleg function
Injective monotone
Majorization
Uncertainty preorder
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