Archivio della ricerca di Triestehttps://arts.units.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 08 Mar 2021 00:36:55 GMT2021-03-08T00:36:55Z10971Continuity and continuous multi-utility representations of nontotal preorders: some considerations concerning restrictivenesshttp://hdl.handle.net/11368/2955601.1Titolo: Continuity and continuous multi-utility representations of nontotal preorders: some considerations concerning restrictiveness
Abstract: A continuous multi-utility fully represents a not necessarily total preorder on a topological space by means of a family of continuous increasing functions. While it is very attractive for obvious reasons, and therefore it has been applied in different contexts, such as expected utility for example, it is nevertheless very restrictive. In this paper we first present some general characterizations of the existence of a continuous order-preserving function, and respectively a continuous multi-utility representation, for a preorder on a topological space. We then illustrate the restrictiveness associated to the existence of a continuous multi-utility representation, by referring both to appropriate continuity conditions which must be satisfied by a preorder admitting this kind of representation, and to the Hausdorff property of the quotient order topology corresponding to the equivalence relation induced by the preorder. We prove a very restrictive result, which may concisely described as follows: the continuous multi-utility representability of all closed (or equivalently weakly continuous) preorders on a topological space is equivalent to the requirement according to which the quotient topology with respect to the equivalence corresponding to the coincidence of all continuous functions is discrete.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11368/2955601.12020-01-01T00:00:00ZOn continuous multi-utility representations of semi-closed and closed preordershttp://hdl.handle.net/11368/2855977Titolo: On continuous multi-utility representations of semi-closed and closed preorders
Abstract: On the basis of the classical continuous multi-utility representation theorem of
Levin on locally compact and $\sigma$-compact Hausdorff spaces, we present necessary and sufficient conditions on a topological space $(X,t)$ under which every semi-closed and closed
preorder respectively admits a continuous multi-utility representation. This discussion provides the fundaments of a mainly topological
theory that systematically combines topological and order theoretic aspects of the
continuous multi-utility representation problem.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11368/28559772016-01-01T00:00:00ZRichter–Peleg multi-utility representations of preordershttp://hdl.handle.net/11368/2865746Titolo: Richter–Peleg multi-utility representations of preorders
Abstract: The existence of a Richter–Peleg multi-utility representation of a preorder by means of upper semicontinuous or continuous functions is discussed in connection with the existence of a Richter–Peleg utility representation. We give several applications that include the analysis of countable Richter–Peleg multi-utility representations.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11368/28657462016-01-01T00:00:00ZContinuous representability of interval orders: The topological compatibility settinghttp://hdl.handle.net/11368/2846707Titolo: Continuous representability of interval orders: The topological compatibility setting
Abstract: In this paper, we go further on the problem of the continuous numerical representability
of interval orders defined on topological spaces. A new condition of compatibility between
the given topology and the indifference associated to the main trace of an interval order
is introduced. Provided that this condition is fulfilled, a semiorder has a continuous
interval order representation through a pair of continuous real-valued functions. Other
necessary and sufficient conditions for the continuous representability of interval orders
are also discussed, and, in particular, a characterization is achieved for the particular
case of interval orders defined on a topological space of finite support.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11368/28467072015-01-01T00:00:00ZNormally preordered spaces and continuous multi-utilitieshttp://hdl.handle.net/11368/2872586Titolo: Normally preordered spaces and continuous multi-utilities
Abstract: We study regular, normal and perfectly normal preorders by referring
to suitable assumptions concerning the preorder and the topology of the space. We also present conditions for the existence of a countable continuous multi-utility representation, hence a Richter-Peleg multi- utility representation, by assuming the existence of a countable net weight.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11368/28725862016-01-01T00:00:00ZREPRESENTATION OF AN INTERVAL ORDER BY MEANS OF TWO UPPER SEMICONTINUOUS FUNCTIONShttp://hdl.handle.net/11368/2345712Titolo: REPRESENTATION OF AN INTERVAL ORDER BY MEANS OF TWO UPPER SEMICONTINUOUS FUNCTIONS
Abstract: In this paper we provide a characterization of the existence of a pair (u,v) of upper semicontinuous real-valued functions
representing an interval order on a topological space
(X,t). The famous Rader's utility representation theorem appears as a corollary of our main result.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11368/23457122011-01-01T00:00:00ZWeak continuity of preferences withnontransitive indifferencehttp://hdl.handle.net/11368/2397067Titolo: Weak continuity of preferences withnontransitive indifference
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11368/23970672011-01-01T00:00:00ZUpper semicontinuous representations of interval ordershttp://hdl.handle.net/11368/2752308Titolo: Upper semicontinuous representations of interval orders
Abstract: Given an interval order on a topological space, we
characterize its representability by means of a pair of upper semicontinuous real-valued functions. This characterization is only based on separability and continuity conditions related to both the interval order and one of its two traces. As a corollary, we obtain the classical Rader's theorem concerning the existence of an upper semicontinuous representation for an upper semicontinuous total preorder on a second countable topological space.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11368/27523082014-01-01T00:00:00ZTopologies corresponding to continuous representability of preordershttp://hdl.handle.net/11368/2355934Titolo: Topologies corresponding to continuous representability of preorders
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11368/23559342010-01-01T00:00:00ZRepresentation of a preorder on a topological space by a countable family of upper semicontinuous order-preserving functionshttp://hdl.handle.net/11368/2924978Titolo: Representation of a preorder on a topological space by a countable family of upper semicontinuous order-preserving functions
Abstract: We discuss the existence of a countable family of upper semicontinuous order-preserving
functions representing a not necessarily total preorder on a topological space.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11368/29249782018-01-01T00:00:00Z