Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Construction of admissible linear orders for pairs of intervals

In this work we construct linear orders between pairs of intervals by using aggregation functions. We apply these orders in a decision-making problem where the experts provide their opinions by means of interval-valued fuzzy sets

Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.The work has been supported by projects TIN2013-40765-P and MTM2012-37894-C02-02 of the Spanish Ministry of Science and the Research Services of the Universidad Publica de Navarra

New trends on the numerical representability of semiordered structures

[EN] We introduce a survey, including the historical back-ground, on different techniques that have recently been issued in the search for a characterization of the representability of semiordered structures, in the sense of Scott and Suppes, by means of a real-valued function and a strictly positive threshold of discrimination.This work has been supported by the research projects MTM2007-62499, ECO2008-01297, MTM2009-12872-C02-02 and MTM2010-17844 (Spain)Abrísqueta, F.; Campión, M.; Catalán, R.; De Miguel, J.; Estevan, A.; Induráin, E.; Zudaire, M.... (2012). New trends on the numerical representability of semiordered structures. Mathware & Soft Computing Magazine. 19(1):25-37. http://hdl.handle.net/10251/57632S253719

Lazy functional algorithms for exact real functionals:23rd International Symposium, MFCS'98 Brno, Czech Republic, August 24–28, 1998 Proceedings

. We show how functional languages can be used to write programs for real-valued functionals in exact real arithmetic. We concentrate on two useful functionals: definite integration, and the functional returning the maximum value of a continuous function over a closed interval. The algorithms are a practical application of a method, due to Berger, for computing quantifiers over streams. Correctness proofs for the algorithms make essential use of domain theory. 1 Introduction In exact real number computation, infinite representations of reals are employed to avoid the usual rounding errors that are inherent in floating point computation [4--6, 17]. For certain real number computations that are highly sensitive to small variations in the input, such rounding errors become inordinately large and the use of floating-point algorithms can lead to completely erroneous results [1, 14]. In such situations, exact real number computation provides guaranteed correctness, although at the (probably..