**DECISIONES RACIONALES Y BIENESTAR SOCIAL: FUNDAMENTOS Y APLICACIONES**

ECO2015-65031-R

•

**Nombre agencia financiadora**Ministerio de Economía y Competitividad

**Acrónimo agencia financiadora**MINECO

**Programa**Programa Estatal de I+D+I Orientada a los Retos de la Sociedad

**Subprograma**Todos los retos

**Convocatoria**Proyectos de I+D+I dentro del Programa Estatal Retos de la Sociedad (2015)

**Año convocatoria**2015

**Unidad de gestión**Dirección General de Investigación Científica y Técnica

**Centro beneficiario**UNIVERSIDAD PÚBLICA DE NAVARRA (UPNA)

**Centro realización**DEPARTAMENTO DE ECONOMÍA

**Identificador persistente**http://dx.doi.org/10.13039/501100003329

## Publicaciones

Found(s) 25 result(s)

Found(s) 1 page(s)

Found(s) 1 page(s)

#### Weightable quasi-metrics related to fuzzy sets

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- García Catalán, Olga Raquel
- Induráin Eraso, Esteban
- Valero, Óscar

We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric., This work has been partially supported by the research projects TIN2013-47605-P, TIN2014-56381-REDT, ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2016-81731-REDT, TIN2016-77356-P (MINECO/ AEI-FEDER, UE) and the Research Services of the Public University of Navarre (Spain).

#### An axiomatic approach to finite means

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- García Catalán, Olga Raquel
- Induráin Eraso, Esteban
- Candeal, Juan Carlos
- Giarlotta, Alfio

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications., This work has been partially supported by the research projects S2013/ICE-2845, ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2015-66471-P (MINECO/ AEI-FEDER, UE), TIN2016-77356-P (MINECO/ AEI-FEDER, UE).

**Proyecto:**MINECO, MINECO, MINECO, ES/1PE/ECO2015-65031-R, MTM2015-63608-P, TIN2015-66471-P, TIN2016-77356-P

#### On the aversion to incomplete preferences

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Hualde Vidaurre, Mikel
- Bourgeois-Gironde, Sacha

We propose an axiomatization of aversion to incomplete preferences. Some prevailing models of incomplete preferences rely on the hypothesis that incompleteness is temporary and that by keeping their opportunity set open individuals reveal a preference for flexibility. We consider that the maintenance of incomplete preference is also aversive. Our model allows us to show how incompleteness induces an aversive attitude in two different ways: intrinsic and instrumental. Intrinsic aversion holds when one instance of incomplete preference in the set suffices to decrease its utility. Instrumental aversion holds only insofar dominating options are affected by incompleteness. Given two partially overlapping sets of axioms on the binary relation over sets we formalize their consistency with the two types of aversion to incompleteness. Finally, we relate our model to the classical Sen's distinction between tentative and assertive incompleteness. The spelling out of this distinction in the terms of our approach uncovers to what extent aversion to incompleteness may be compatible with a preference for flexibility., Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) and the Public University of Navarre is acknowledged.

**Proyecto:**MINECO//ECO2015-65031-R

#### Geometrical aggregation of finite fuzzy sets

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- García Catalán, Olga Raquel
- Induráin Eraso, Esteban
- Lizasoain Iriso, María Inmaculada
- Raventós Pujol, Armajac
- Valero, Óscar

A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting., This work has been partially supported by the research projects TIN2013-47605-P, ECO2015-65031-R, MTM2015-63608-P (MINECO/AEI-FEDER, UE), TIN2016-77356-P (MINECO/AEI-FEDER, UE) and TIN2016-81731-REDT (LO-DISCO II and MINECO/AEI-FEDER, UE).

#### Fair competition design

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Dimitrov, Dinko

We study the impact of two basic principles of fairness on the

structure of competition systems and perform our analysis by focusing on sports competitions. The first principle states that equally

strong players should have the same chances of being the final winner, while the second principle requires that the competition system

should not favor weaker players. We apply these requirements to a

class of competitions which includes, but is not limited to, the sport

tournament systems that are most commonly used in practice, such

as round-robin tournaments and different kinds of knockout competitions, and we characterize the structures satisfying these requirements. In our results, a new competition structure that we call an antler is

found to play a referential role. Finally, we show that the class of fair

competition systems becomes rather small when both fairness principles are jointly applied., Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) is

acknowledged.

structure of competition systems and perform our analysis by focusing on sports competitions. The first principle states that equally

strong players should have the same chances of being the final winner, while the second principle requires that the competition system

should not favor weaker players. We apply these requirements to a

class of competitions which includes, but is not limited to, the sport

tournament systems that are most commonly used in practice, such

as round-robin tournaments and different kinds of knockout competitions, and we characterize the structures satisfying these requirements. In our results, a new competition structure that we call an antler is

found to play a referential role. Finally, we show that the class of fair

competition systems becomes rather small when both fairness principles are jointly applied., Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) is

acknowledged.

**Proyecto:**MINECO//ECO2015-65031-R

#### League competitions and fairness

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Dimitrov, Dinko

We formulate two fairness principles and characterize the league competition systems that satisfy them. The first principle requires that all players should have the same chance of being the final winner if all players are equally strong, while the second states that the league competition should not favor weaker players. We apply these requirements to a class of systems which includes round-robin tournaments as a particular case., Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) is acknowledged. Open Access funding enabled and organized by Projekt DEAL.

**Proyecto:**MINECO//ECO2015-65031-R

#### Partial representations of orderings

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Bosi, Gianni
- Zuanon, Magali
- Estevan Muguerza, Asier

In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner, avoiding any unnecessary information. For this purpose, the new concept of representability is developed by means of partial functions, so that other common definitions of representability (i.e. (Richter-Peleg) multi-utility, Scott-Suppes representability, … ) are now particular cases in which the partial functions are actually functions. The paper also presents a collection of examples and propositions showing the advantages of this kind of representations, particularly in the case of partial orders and semiorders, as well as some results showing the connections between distinct kinds of representations., Asier Estevan acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under grants MTM2012-37894-C02-02, MTM2015-63608-P and ECO2015-65031 as well as from the Basque Government under grant IT974-16. Gianni Bosi and Magali E. Zuanon acknowledge financial support from the Istituto Nazionale di Alta Matematica 'F. Severi' (Italy).

#### Fair elimination-type competitions

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Dimitrov, Dinko

We study the impact of two basic principles of fairness on the structure of elimination-type competitions and perform our analysis by focusing on sports competitions. The first principle states that stronger players should have a larger chance of winning than weaker players, while the second principle provides equally strong players the same chances of being the final winner. We apply these requirements to different kinds of knockout competitions, and characterise the structures satisfying them. In our results, a new competition structure that we call an antler is found to play a referential role., This work was supported by the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE).

**Proyecto:**MINECO//ECO2015-65031-R

#### Power set extensions of dichotomous preferences

Power set extensions of dichotomous preferences-->##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Dimitrov, Dinko

This paper is devoted to the study of how to extend a dichotomous

partition of a universal set X into good and bad objects to an ordering

on the power set of X. We introduce a family of rules that naturally

take into account the number of good objects and the number of bad

objects, and provide axiomatic characterizations of two rules that are

particularly appealing when it comes to compating sets in which the

good, R. Arlegi

gratefully acknowledges financial support from the Spanish Ministry of Education,

projects ECO2012-34202 and ECO2015-65031-R.

partition of a universal set X into good and bad objects to an ordering

on the power set of X. We introduce a family of rules that naturally

take into account the number of good objects and the number of bad

objects, and provide axiomatic characterizations of two rules that are

particularly appealing when it comes to compating sets in which the

good, R. Arlegi

gratefully acknowledges financial support from the Spanish Ministry of Education,

projects ECO2012-34202 and ECO2015-65031-R.

#### Topologies for semicontinuous Richter–Peleg multi-utilities

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Bosi, Gianni
- Estevan Muguerza, Asier
- Raventós Pujol, Armajac

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., 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.

#### Aggregation of individual rankings through fusion functions: criticism and optimality analysis

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Bustince Sola, Humberto
- Bedregal, Benjamin
- Campión Arrastia, María Jesús
- Fernández Fernández, Francisco Javier
- Induráin Eraso, Esteban
- Raventós Pujol, Armajac
- Silva, Ivanoska da
- Santiago, Regivan

Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice where well-known impossibility results as the Arrovian ones are encountered and the decision-making approaches where the necessity of fusing rankings is unavoidable. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings IEEE., This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2016-77356-P (MINECO/ AEI-FEDER, UE), PID2019-108392GB-I00 (AEI/10.13039/501100011033), and Brazilian National Council for Scientific and Technological Development CNPq (Proc. 307781/2016-0).

#### On the structure of acyclic binary relations

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Rodríguez Alcantud, José Carlos
- Candeal, Juan Carlos
- Campión Arrastia, María Jesús
- García Catalán, Olga Raquel
- Induráin Eraso, Esteban

We investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representation by means of incidence matrices. Acyclic binary relations can be extended to the asymmetric part of a linear order, so that, in particular, any directed acyclic graph has a topological sorting., This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P, ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain).

**Proyecto:**ES, ES, MINECO, ES/6PN, 1PE, 1PE/MTM2012-37894, TIN2013-47605, ECO2015-65031-R, TIN2016-77356-P

#### Participation in and provision of public goods: Does granularity matter?

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Benito Ostolaza, Juan Miguel
- Osés Eraso, Nuria

We use public goods games to experimentally investigate the effect of granularity (i.e., the degree of divisibility of the space of feasible contribution options) on participation (whether individuals contribute or not to the public good) and public goods provision (total contribution to the public good). Our results show that granularity has a significant effect on participation, mainly when coarser granularity eliminates the possibility of small contributions. However, this change in participation does not lead to a significant change in the total provision of the public good. These results are aligned with other experimental field results obtained in the context of donations and fundraising., This work was supported by the Spanish Ministry of Economy and Competitiveness (Grant Number ECO2015-65031-R).

**Proyecto:**MINECO//ECO2015-65031-R

#### Sports betting and the Black-Litterman model: a new portfolio-management perspective

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Abinzano Guillén, María Isabel
- Campión Arrastia, María Jesús
- Muga Caperos, Luis Fernando
- Raventós Pujol, Armajac

This paper transfers and adapts the Black-Litterman portfolio management model and its subsequent generalizations to the characteristics and specificities of assets quoted on sports betting markets. The results show that these assets are suitable for the application of portfolio management models with possible inclusion of investors' opinions. Information based on the variability of market prices and the attention received by NBA teams in Google Trends is successfully used to simulate the opinions expressed by a hypothetical portfolio manager. Furthermore, this makes these assets suitable for inclusion in portfolios in which managers are seeking returns uncorrelated with other assets., Financial support from the Spanish Ministry of Economy and Competitiveness, (ECO 2015-65031-R and ECO2016-77631-R); Spanish Ministry of Science and Innovation (PID2019-104304GB-I00/AEI/10.13039/501100011033) and Fundación Caja Navarra FUNCAN-07445 are gratefully acknowledged.

#### Risk attitudes in medical decisions for others: an experimental approach

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arrieta, Alejandro
- González, Paula
- Pinto Prades, José Luis
- García Prado, Ariadna

The aim of this paper is to investigate how risk attitudes in medical decisions for others vary across health contexts. A lab experiment was designed to elicit the risk attitudes of 257 medical and nonmedical students by assigning them the role of a physician who must decide between treatments for patients. An interval regression model was used to estimate individual coefficients of relative risk aversion, and an estimation model was used to test for the effect of type of medical decision and experimental design characteristics on elicited risk aversion. We find that (a) risk attitudes vary across different health contexts, but risk aversion prevails in all of them; (b) students enrolled in health‐related degrees show a higher degree of risk aversion; and (c) real rewards for third parties (patients) make subjects less risk‐averse. The results underline the importance of accounting for attitudes towards risk in medical decision making., Ministerio de Ciencia y Tecnología and FEDER, Grant numbers: ECO2012‐3648, ECO2013‐43526‐R, ECO2015‐65031‐R and ECO2015‐65408‐R; Junta de Andalucía, Grant number: SEJ‐04992

**Proyecto:**MINECO, MINECO, MINECO, MINECO//ECO2012-36480, ECO2013-43526-R, ECO2015-65031-R, ECO2015-65408-R

#### Automatic detection of high-voltage power lines in LiDAR surveys using data mining techniques

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Chasco Hernández, Daniel
- García Morales, Víctor
- Sanz Delgado, José Antonio
- Álvarez-Mozos, Jesús

The correct classification of power lines in LiDAR point clouds has attracted the interest of the mapping community in the last years. The objective of this research is the detection and automatic extraction of high-voltage transmission lines from LiDAR data using data mining techniques. With this aim, a Single Photon LiDAR (SPL) survey acquired over the region of Navarre (Spain) in 2017 was used, with a mean point density of 14 pt/m2. Different data mining techniques were evaluated, including decision trees (C4.5 and CART) and ensemble learning algorithms (Random Forests, Bagging and AdaBoost). Fifteen test sites were studied corresponding to areas with high-voltage power lines over different conditions regarding the underlying vegetation and topography. For these sites 92,104 LiDAR points were identified as power lines and more than 4M points as not power lines using existing cartography. This dataset was randomly split in train and test sets and then balanced two obtain a similar amount of data for the two classes. The results obtained show the importance of balancing the training data with improvements in accuracy of ~10% with respect to the imbalanced case. Accuracies higher than 87% were obtained in all balanced cases, with particularly successful results for ensemble learning techniques, being AdaBoost the technique with the highest accuracy 91%. These results suggest that the combination of SPL surveys and data mining tools can be successfully used for the operational mapping of high voltage power lines., The Government of Navarre and Tracasa are acknowledged for the provision of the SPL LiDAR data, the TerraScan software license and their expertise.

#### Searching for a Debreu’s open gap lemma for semiorders

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Estevan Muguerza, Asier

In 1956 R. D. Luce introduced the notion of a semiorder to deal with indifference relations in the representation of a preference. During several years the problem of finding a utility function was studied until a representability characterization was found. However, there was almost no results on the continuity of the representation. A similar result to Debreu’s Lemma, but for semiorders was never achieved. In the present paper we propose a characterization for the existence of a continuous representation (in the sense of Scott-Suppes) for bounded semiorders. As a matter of fact, the weaker but more manageable concept of ε-continuity is properly introduced for semiorders. As a consequence of this study, a version of the Debreu’s Open Gap Lemma is presented (but now for the case of semiorders) just as a conjecture, which would allow to remove the open-closed and closed-open gaps of a subset S ⊆ R, but now keeping the constant threshold, so that x + 1 < y if and only if g(x) + 1 < g(y) (x, y ∈ S)., The author acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under grants MTM2015-63608-P and ECO2015-65031.

#### A survey on the mathematical foundations of axiomatic entropy: representability and orderings

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- Gómez Polo, Cristina
- Induráin Eraso, Esteban
- Raventós Pujol, Armajac

Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations., This work was partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/AEI-FEDER, UE), 0011-1365-2016-000060, PC003-004-005 DRUG-MAG, TIN2016-77356-P (MINECO/AEI-FEDER, UE) and 0011-1365-2017-000118.

#### Binary relations coming from solutions of functional equations: orderings and fuzzy subsets

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- Miguel Turullols, Laura de
- García Catalán, Olga Raquel
- Induráin Eraso, Esteban
- Abrísqueta Usaola, Francisco Javier

Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 25, Suppl. 1 (December 2017) 19-42 DOI: 10.1142/S0218488517400025 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijufks, We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical

representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set., This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P,

ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain).

representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set., This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P,

ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain).

#### Multidistances and inequality measures on abstract sets: an axiomatic approach

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- Induráin Eraso, Esteban
- Raventós Pujol, Armajac
- Díaz, Irene
- Martín, Javier
- Mayor, Gaspar
- Montes Rodríguez, Susana

Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among inequality measures, apart from multidistances we pay special attention to dispersions, and study their main features. Classical concepts will be generalized to this abstract setting. Multidistances are then revisited, and some new methods to generate them are implemented. A wide spectrum of interdisciplinary applications is outlined in the final section., This work is partially supported by the research projects ECO2015-65031-R , MTM2015-63608-P , TIN2016-77356-P , TIN2017-87600-P (MINECO/AEI-FEDER, UE) and PID2019-108392GB-I00 (AEI/10.13039/501100011033)

#### Continuous representations of interval orders by means of two continuous functions

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Bosi, Gianni
- Estevan Muguerza, Asier

In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case by means of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases., 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. Sever' (Italy).

#### Pareto rationalizability by two single-peaked preferences

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Arlegi Pérez, Ricardo
- Teschl, Miriam

We study, in a finite setting, the problem of Pareto rationalizability of choice functions by means of a preference profile that is single-peaked with respect to an exogenously given linear order over the alternatives. This problem requires a new condition to be added to those that characterize Pareto rationalizability in the general domain of orders (Moulin (1985)). This new condition appeals to the existence of a central range of options such that the choice function excludes alternatives which are distant from that range., We acknowledge financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) and the Austrian Science Fund (FWF T366-G14).

**Proyecto:**MINECO//ECO2015-65031-R

#### Assigning numerical scores to linguistic expressions

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- Campión Arrastia, María Jesús
- Falcó Díaz de Cerio, Edurne
- Induráin Eraso, Esteban
- García Lapresta, José

In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed., This work has been partially supported by the Spanish Ministerio de Economía y Competitividad (projects ECO2015-65031-R, MTM2015-63608-P, ECO2016-77900-P and TIN2016-77356-P), ERDF and the Research Services of the Universidad Pública de Navarra (Spain). Thanks are also given to Remedios Marín and Íñigo Arozarena (Departamento de Tecnología de Alimentos, Universidad Pública de Navarra, Pamplona, Spain) for their valuable suggestions and comments.

**Proyecto:**MINECO, MINECO, ES, ES/1PE, 1PE/ECO2015-65031-R, MTM2015-63608-P, ECO2016-77900, TIN2016-77356

#### Changes in muscle power after usual care or early structured exercise intervention in acutely hospitalized older adults

##### Academica-e. Repositorio Institucional de la Universidad Pública de Navarra

- López Sáez de Asteasu, Mikel
- Martínez Velilla, Nicolás
- Zambom Ferraresi, Fabrício
- Ramírez Vélez, Robinson
- Casas Herrero, Álvaro
- Galbete Jiménez, Arkaitz
- Izquierdo Redín, Mikel
- García Hermoso, Antonio
- Cadore, Eduardo L.

Background: A classic consequence of short-term bed rest in older adults is the significant loss in skeletal muscle mass and muscle strength that underlies the accelerated physical performance deficits. Structured exercise programmes applied during acute hospitalization can prevent muscle function deterioration. Methods: A single-blind randomized clinical trial conducted in an acute care for elders unit in a tertiary public hospital in Navarre (Spain). Three hundred seventy hospitalized patients [56.5% female patients; mean age (standard deviation) 87.3 (4.9) years] were randomly allocated to an exercise intervention (n = 185) or a control (n = 185) group (usual care). The intervention consisted of a multicomponent exercise training programme performed during 5–7 consecutive days (2 sessions/day). The usual-care group received habitual hospital care, which included physical rehabilitation when needed. The main endpoints were change in maximal dynamic strength (i.e. leg-press, chest-press, and knee extension exercises) and maximal isometric knee extensors and hip flexors strength from baseline to discharge. Changes in muscle power output at submaximal and maximal loads were also measured after the intervention. Results: The physical exercise programme provided significant benefits over usual care. At discharge, the exercise group showed a mean increase of 19.6 kg [95% confidence interval (CI), 16.0, 23.2; P < 0.001] on the one-repetition maximum (1RM) in the leg-press exercise, 5.7 kg (95% CI, 4.7, 6.8; P < 0.001) on the 1RM in the chest-press exercise, and 9.4 kg (95% CI, 7.3, 11.5; P < 0.001) on the 1RM in the knee extension exercise over usual-care group. There were improvements in the intervention group also in the isometric maximal knee extension strength [14.8 Newtons (N); 95% CI, 11.2, 18.5 vs. −7.8 N; 95% CI, −11.0, −3.5 in the control group; P < 0.001] and the hip flexion strength (13.6 N; 95% CI, 10.7, 16.5 vs. −7.2 N; 95% CI, −10.1, −4.3; P < 0.001). Significant benefits were also observed in the exercise group for the muscle power output at submaximal loads (i.e. 30% 1RM, 45% 1RM, 60% 1RM, and 75% 1RM; all P < 0.001) over usual-care group. Conclusions: An individualized, multicomponent exercise training programme, with special emphasis on muscle power training, proved to be an effective therapy for improving muscle power output of lower limbs at submaximal loads and maximal muscle strength in older patients during acute hospitalization., This study was funded by a Gobierno de Navarra project grant (Resolución 2186/2014) and acknowledged with the 'Beca Ortiz de Landazuri' for the best research clinical project in 2014, as well as by a research grant PI17/01814 of the Ministerio de Economía, Industria y Competitivad (ISCIII, FEDER). The authors thank Fundación Miguel Servet (Navarrabiomed) for its support during the implementation of the trial, as well as Fundación Caja Navarra and Fundación la Caixa. R.R.-V. is funded in part by a postdoctotal fellowship grant ID 420/2019 of the Public University of Navarre, Spain.

#### An axiomatic approach to finite means

##### Zaguán. Repositorio Digital de la Universidad de Zaragoza

- Campión, M.J.
- Candeal, J.C.
- Catalán, R.G.
- Giarlotta, A.
- Greco, S.
- Induráin, E.
- Montero, J.

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.