Artículos de revista INARBE - INARBE aldizkari artikuluak

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Open Access
An axiomatic approach to finite means
(Elsevier, 2018) Campión Arrastia, María Jesús; Candeal, Juan Carlos; García Catalán, Olga Raquel; Giarlotta, Alfio; Induráin Eraso, Esteban; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
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.
Open Access
Decomposition and arrow-like aggregation of fuzzy preferences
(MDPI, 2020) Raventós Pujol, Armajac; Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.
Open Access
Decomposition of fuzzy relations: an application to the definition, construction and analysis of fuzzy preferences
(MDPI, 2023) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE
In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences.
Open Access
An extended behavior model for explaining the willingness to pay to reduce the air pollution in road transportation
(Elsevier, 2021) Sánchez García, Mercedes; Zouaghi, Ferdaous; Lera López, Fernando; Faulín Fajardo, Javier; Enpresen Kudeaketa; Ekonomia; Estatistika, Informatika eta Matematika; Institute on Innovation and Sustainable Development in Food Chain - ISFOOD; Institute for Advanced Research in Business and Economics - INARBE; Institute of Smart Cities - ISC; Gestión de Empresas; Economía; Estadística, Informática y Matemáticas
Road transportation constitutes a key sector in developed countries, as an essential catalyst for economic and social activities. Nevertheless, it is relevant to emphasize the negative impacts of this activity identified in Economics as negative externalities. At the European Union, road transportation is the main cause of the air pollution impact on the population. Thus, this study explores the factors that influence the willingness to pay (WTP) on behalf of the citizens to reduce air pollution generated by road transport. In doing so, we propose two fundamental theoretical frameworks to explain individual behavior towards the environment actions: the Theory of Planned Behavior (TPB) and the Value-Belief-Norm (VBN) models. A questionnaire survey with 1,612 residents was used to collect data in 65 localities located in the Spanish Pyrenees and performing a statistical analysis with the resulting data relied on application of Structural Equation Models (SEM). Moreover, the survey results highlight the importance of psychological aspects as predictors of proenvironmental behaviors. Our empirical results provide a novel contribution about how governments and educational policies can enhance the positive attitude towards environmental actions, unifying the struggle in favor of environmental protection from early childhood.
Open Access
Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
(MDPI, 2024-08-13) Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Sara Goyen, Martín Sergio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2
We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score.
Open Access
Fuzzy Arrovian theorems when preferences are strongly-connected
(University of Sistan and Baluchestan, 2022) Raventós Pujol, Armajac; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this paper we study the aggregation of fuzzy preferences on non-necessarily finite societies. We characterize in terms of possibility and impossibility a family of models of strongly-connected preferences in which the transitivity is defined for any t-norm. For that purpose, we have described each model by means of some crisp binary relations and we have applied the results obtained by Kirman and Sondermann about ultrafilters and Arrovian models.
Open Access
Geometrical aggregation of finite fuzzy sets
(Elsevier, 2018) Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Lizasoain Iriso, María Inmaculada; Raventós Pujol, Armajac; Valero, Óscar; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y Matemáticas
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.
Open Access
The hidden value of intangibles: do CEO characteristics matter?
(Emerald, 2019) Garcés Galdeano, Lucía; García Olaverri, Carmen; Enpresen Kudeaketa; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Gestión de Empresas; Estadística, Informática y Matemáticas
Purpose: A great deal of research has examined the relationship between a single CEO attribute and a single measure of firm performance; no attempts have been made to integrate them to create a more global vision of both. Therefore, trying to answer new calls from Wang et al. (2016) or Liu, Fisher and Chen (2018) about a more global vision of the CEO characteristics, the authors are going to take a step forward to combine different CEO characteristics with different firm performance measure in order to show that a certain managerial profile would have an impact on several variables of firm performance. This paper aims to discuss these issues. Design/methodology/approach: Using a sample of 1,236 small firms in high- and medium-high-technology sectors and through the Canonical Correlation Analysis, the authors are able to create different CEO’s profiles that influence on different combinations of firm performance variables. Findings: The authors obtain different CEO’s profiles that influence on different combinations of firm performance variables. Each CEO profile will enhance or diminish one kind of performance measure. The authors found that on the one hand, young, well-educated with external experience CEO profile will enhance innovative performance and firm growth, and on the other hand, old and more internal and external experience CEO profile will enhance the exploitation of external knowledge. Originality/value: Through this analysis, the authors will be able to provide a more comprehensive analysis of the predictions about the role of CEOs in small firms.
Open Access
How important is family involvement for small companies’ growth?
(Emerald, 2020) Garcés Galdeano, Lucía; García Olaverri, Carmen; Enpresen Kudeaketa; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Gestión de Empresas; Estadística, Informática y Matemáticas
Purpose: Our paper seeks to further understand how family involvement in management influences firm growth. Design/methodology/approach: Using a sample of small high-tech firms, we classify three different types of firms: family firms managed by family-CEOs, family firms managed by non-family CEOs and non-family firms. Findings: Consistent with our expectations, we show that firms managed by family-CEOs have less firm growth in comparison with the other two groups. When the family firm is managed by non-family CEOs, the presence of another family member in management positions has a negative impact on firm growth. Finally, we found that founder-led family firms have better firm growth than descendant-led family firms. Research limitations/implications: Implications for the theory of family firms are discussed. Originality/value: The value of the present study is to analyse in depth the heterogeneity of the family business trying to close the gap by exploring the effect of family involvement on small firm growth. Thus, we will find different behaviours of these family companies, depending on the family member’s presence in management positions.
Open Access
A mathematical approach to law and deal modelling: legislation and agreements
(MDPI, 2021) Benito Ostolaza, Juan Miguel; Campión Arrastia, María Jesús; Estevan Muguerza, Asier; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Social norms are a set of rules to be followed by the people of a community in order to have a better coexistence, to which the behaviors, tasks, and activities of the human being must be adjusted. The set or system of norms, rules, or duties regulates the actions of individuals among themselves. This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations. This is done by giving a mathematical formalization to the set of all possible agreements or regulations, so that, then, the proximity between them is defined by means of a premetric. Thanks to this mathematical structure that tries to capture the problematic of agreements and modifications of regulations, some currently issues related to game theory or law are now reduced to mathematical optimization problems.
Open Access
Multidistances and inequality measures on abstract sets: an axiomatic approach
(Elsevier, 2021) Campión Arrastia, María Jesús; Díaz, Irene; Induráin Eraso, Esteban; Martín, Javier; Mayor, Gaspar; Montes Rodríguez, Susana; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y Matemáticas
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.
Embargo
A new approach to continuous assessment: moving from a stressful sum of grades to meaningful learning through self-reflection
(Elsevier, 2024-11-01) Rodríguez Rincón, Yeray; Munárriz Iriarte, Ana; Magreñán Ruiz, Ángel Alberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE
This paper proposes a new approach of continuous assessment of a formative nature, aimed at achieving meaningful learning with lower stress levels. This approach minimizes the punitive nature of traditional summative continuous assessment and replaces typical graded activities with self-reflecting ones. To conduct the formative evaluation, a teaching model has been developed to guide the choice of feedback and feed-forward strategies to be implemented by the instructors, depending on the students¿ levels of competence and confidence. To validate the effectiveness of this approach, a quasi-experimental design was employed, with the new continuous assessment method in the experimental group and the summative continuous assessment method in the control group. The experiment was conducted in a Mathematics course with undergraduate Economics and Business students. Data were collected through test scores and a perception questionnaire. The results indicate that the new evaluation method promotes meaningful learning and yields better academic results compared to the traditional continuous evaluation. Students expressed high satisfaction with the new approach, noting that it allows them to understand their formative status and address deficiencies before undertaking evaluable activities. They also believe this strategy helps reduce the stress associated with the summative evaluation itself.
Open Access
Plant ammonium sensitivity is associated with external pH adaptation, repertoire of nitrogen transporters, and nitrogen requirement
(Oxford University Press, 2024-03-11) Rivero Marcos, Mikel; Lasa Larrea, Berta; Neves, Tomé; Zamarreño, Ángel M.; García Mina, José M.; García Olaverri, Carmen; Aparicio Tejo, Pedro María; Cruz, Cristina; Ariz Arnedo, Idoia; Ciencias; Zientziak; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Multidisciplinary Research in Applied Biology - IMAB; Institute for Advanced Research in Business and Economics - INARBE; Universidad Publica de Navarra / Nafarroako Unibertsitate Publikoa; Gobierno de Navarra / Nafarroako Gobernua
Modern crops exhibit diverse sensitivities to ammonium as the primary nitrogen source, influenced by environmental factors such as external pH and nutrient availability. Despite its significance, there is currently no systematic classification of plant species based on their ammonium sensitivity. We conducted a meta-analysis of 50 plant species and present a new classification method based on the comparison of fresh biomass obtained under ammonium and nitrate nutrition. The classification uses the natural logarithm of the biomass ratio as the size effect indicator of ammonium sensitivity. This numerical parameter is associated with critical factors for nitrogen demand and form preference, such as Ellenberg indicators and the repertoire of nitrogen transporters for ammonium and nitrate uptake. Finally, a comparative analysis of the developmental and metabolic responses, including hormonal balance, is conducted in two species with divergent ammonium sensitivity values in the classification. Results indicate that nitrate has a key role in counteracting ammonium toxicity in species with a higher abundance of genes encoding NRT2-type proteins and fewer of those encoding the AMT2-type proteins. Additionally, the study demonstrates the reliability of the phytohormone balance and methylglyoxal content as indicators for anticipating ammonium toxicity. This study emphasizes the importance of ecophysiological requirements and the repertoire of nitrogen transporters in understanding plant sensitivity to ammonium, and enhances our knowledge of plant nitrogen nutrition.
Open Access
Quasi-metrics for possibility results: intergenerational preferences and continuity
(MDPI, 2023) Estevan Muguerza, Asier; Maura, Roberto; Valero, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa JIUPNA19-2022
In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved.
Embargo
Scores of hesitant fuzzy elements revisited: "Was sind und was sollen"
(Elsevier, 2023) Alcantud, José Carlos R.; Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE
This paper revolves around the notion of score for hesitant fuzzy elements, the constituent parts of hesitant fuzzy sets. Scores allow us to reduce the level of uncertainty of hesitant fuzzy sets to classical fuzzy sets, or to rank alternatives characterized by hesitant fuzzy information. We propose a rigorous and normative definition capable of encapsulating the characteristics of the most important scores introduced in the literature. We systematically analyse different types of scores, with a focus on coherence properties based on cardinality and monotonicity. The hesitant fuzzy elements considered in this analysis are unrestricted. The inspection of the infinite case is especially novel. In particular, special attention will be paid to the analysis of hesitant fuzzy elements that are intervals.
Open Access
Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold
(Elsevier, 2023) Estevan Muguerza, Asier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, JIUPNA19-2022
The problem of finding a utility function for a semiorder has been studied since 1956, when the notion of semiorder was introduced by Luce. But few results on continuity and no result like Debreu’s Open Gap Lemma, but for semiorders, was found. In the present paper, we characterize semiorders that accept a continuous representation (in the sense of Scott–Suppes). Two weaker theorems are also proved, which provide a programmable approach to Open Gap Lemma, yield a Debreu’s Lemma for semiorders, and enable us to remove the open-closed and closed-open gaps of a set of reals while keeping the threshold.
Open Access
A survey on the mathematical foundations of axiomatic entropy: representability and orderings
(MDPI, 2018) Campión Arrastia, María Jesús; Gómez Polo, Cristina; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Zientziak; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Ciencias
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.
Open Access
Topologies for semicontinuous Richter–Peleg multi-utilities
(Springer, 2020) Bosi, Gianni; Estevan Muguerza, Asier; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y Matemáticas
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.
Open Access
What do law and mathematics have in common? The sustainable development goals as a transversal substrate of numbers and laws
(CEUR-WS, 2022) Chicharro Lázaro, Alicia; Campión Arrastia, María Jesús; Derecho; Zuzenbidea; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Social Research - ICOMMUNITAS
This paper presents two experiences of innovative teaching at the Public University of Navarra that have as a fundamental common link: the mainstreaming of the Sustainable Development Goals in the curriculum. With this objective in mind, the subjects International Law and Mathematics, that are a priori conceptually different, can be worked on at a competency level with the same common challenge. This challenge consists in promoting the exercise of global citizenship, active, supportive, responsible, and committed to sustainable development. For both experiences, some of the activities carried out with this objective are described, contextualized in the framework of the Sustainable Development Goals (SDGs). The main conclusions drawn from the experience are analyzed, highlighting the fundamental role of universities as a driving force for social transformation from different dimensions.

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