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    Topologies for semicontinuous Richter–Peleg multi-utilities

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    2020020043_Bosi_TopologiesSemicontinuous.pdf (190.4Kb)
    Date
    2020
    Author
    Bosi, Gianni 
    Estevan Muguerza, Asier Upna
    Raventós Pujol, Armajac Upna
    Version
    Acceso abierto / Sarbide irekia
    xmlui.dri2xhtml.METS-1.0.item-type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    ES/1PE/MTM2015-63608-P 
    ES/1PE/ECO2015-65031 
    Impact
     
     
     
    10.1007/s11238-019-09730-7
     
     
     
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    Abstract
    The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower (upper) semicontinuous Richter–Peleg mu ... [++]
    The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower (upper) semicontinuous Richter–Peleg multi-utility, then the topology of the space must be finer than the Upper (resp. Lower) topology. However, this condition fails to be sufficient. Instead of search for properties that must be satisfied by the preorder, we study finer topologies which are necessary or/and sufficient for the existence of semicontinuous representations. We prove that Scott topology must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter–Peleg multi-utility. However, the existence of this representation cannot be guaranteed. A sufficient condition is given by means of Alexandroff’s topology, for that, we prove that more order implies less Alexandroff’s topology, as well as the converse. Finally, the paper is implemented with a topological study of the maximal elements. [--]
    Subject
    Preorders, Multi-utility theory, Richter–Peleg, Semicontinuity
     
    Publisher
    Springer
    Published in
    Theory and Decision, 2020, 88, 457-470
    Departament
    Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas / Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. Inarbe - Institute for Advanced Research in Business and Economics
     
    Publisher version
    https://doi.org/10.1007/s11238-019-09730-7
    URI
    https://hdl.handle.net/2454/36990
    Sponsorship
    Asier Estevan acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under Grants MTM2015-63608-P and ECO2015-65031. Gianni Bosi acknowledges financial support from the Istituto Nazionale di Alta Matematica 'F. Severi' (Italy). Armajac Raventos acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under Grant ECO2015-65031.
    Appears in Collections
    • Artículos de revista DEIM - EIMS Aldizkari artikuluak [103]
    • Artículos de revista InaMat - InaMat aldizkari artikuluak [142]
    • Artículos de revista INARBE - INARBE aldizkari artikuluak [50]
    • Artículos de revista - Aldizkari artikuluak [2924]
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