Open Access
Aprender matemáticas: ¿qué enseñan los niños con discapacidad intelectual a los maestros en formación?
(Universidad de Zaragoza, 2019-05-14) Cogolludo, José Ignacio; García Catalán, Olga Raquel; Gil Clemente, Elena; Lizasoain Iriso, María Inmaculada; Millán Gasca, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
La actitud con la que los maestros de Primaria afrontan su tarea como profesores de matemáticas tiene más que ver con sus experiencias previas como alumnos de la disciplina que con los contenidos que han aprendido durante las asignaturas de didáctica de las matemáticas en los Grados de Educación. Esta cuestión tiene un impacto sobre la instrucción matemática posterior de los niños, que se amplifica en el caso de los que tienen necesidades educativas especiales y conduce a emprender vías poco eficaces. Nuestro objetivo es trasladar a los estudiantes prácticas positivas, en forma de experiencia, llevadas a cabo con niños con discapacidad intelectual que puedan iluminarles sobre la forma de aprender de cualquier niño. Prácticas basadas por una parte en un enfoque histórico que propone una integración de aritmética y geometría elementales y por otra parte en el modelo desarrollado en Singapur para la resolución de problemas.
Open Access
Orness for idempotent aggregation functions
(MDPI, 2017) Legarreta, Leire; Lizasoain Iriso, María Inmaculada; Mardones Pérez, Iraide; Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Matemáticas
Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.
Open Access
The interval-valued Choquet integral based on admissible permutations
(IEEE, 2018) Paternain Dallo, Daniel; Miguel Turullols, Laura de; Ochoa Lezaun, Gustavo; Lizasoain Iriso, María Inmaculada; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Aggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, in this work we propose the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.
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
Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition
(Taylor & Francis, 2019) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1
Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in [0, 1]. The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.
Open Access
Orness measurements for lattice m-dimensional interval-valued OWA operators
(Elsevier, 2018) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggegating functions, which obviously give diferent results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are de ned on m-dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator.
Embargo
Some characterizations of lattice OWA operators
(World Scientific Publishing Company, 2017) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa; Matemáticas; Matematika
Ordered Weighted Averaging (OWA) operators are a family of aggregation which fusion data. If the data are real numbers, then OWA operators can be characterized either as an special kind of Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are de ned on a complete lattice. In addition, the set of all n -ary OWA operators is studied as a sublattice of the lattice of all the n -ary aggregation functions de ned on a distributive lattice.
Open Access
Addressing the issue of trust in elementary teachers' maths-specific education: ANFoMAM project
(Charles University (Chequia), 2019) Celi, Valentina; Cogolludo, José Ignacio; Gil Clemente, Elena; Lizasoain Iriso, María Inmaculada; Millán Gasca, Ana; Moler Cuiral, José Antonio; Regoliosi, Luigi; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
To improve primary school teachers' maths-specific education at university, our project will develop a series of workshops, as ready-to-use instruments, which closely consider children's way of learning and their relationship with mathematics. Thus, the interest of participants in children is exploited in sessions which take into account both their professional work as teachers and their own childhood experiences. The aim is to help participants to evolve in the key aspect of trust. The paper describes the objectives and first results of the ANFoMAM project, supported by the Erasmus Plus Programme in the area of strategic partnerships for innovation in higher education in Europe.