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

Author

Listed:
  • Pedro Hack

    (Ulm University)

  • Daniel A. Braun

    (Ulm University)

  • Sebastian Gottwald

    (Ulm University)

Abstract

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.

Suggested Citation

  • Pedro Hack & Daniel A. Braun & Sebastian Gottwald, 2023. "The classification of preordered spaces in terms of monotones: complexity and optimization," Theory and Decision, Springer, vol. 94(4), pages 693-720, May.
    • Handle: RePEc:kap:theord:v:94:y:2023:i:4:d:10.1007_s11238-022-09904-w
    DOI: 10.1007/s11238-022-09904-w
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    References listed on IDEAS

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