Person: Miguel Turullols, Laura de
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Miguel Turullols
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Laura de
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Estadística, Informática y Matemáticas
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ISC. Institute of Smart Cities
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0000-0002-7665-2801
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810922
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Publication 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 PublikoaAggregation 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.Publication Open Access Pointwise aggregation of maps: its structural functional equation and some applications to social choice theory(Elsevier, 2017) Miguel Turullols, Laura de; Campión Arrastia, María Jesús; Candeal, Juan Carlos; Induráin Eraso, Esteban; Paternain Dallo, Daniel; Automática y Computación; Matemáticas; Automatika eta Konputazioa; Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued functions, we characterize several special kinds of aggregation operators as strictly monotone modifications of projections. As a case study, we introduce a first approach of type-2fuzzy sets via fusion operators. We develop some applications and possible uses related to the analysis of properties of social evaluation functionals in social choice, showing that those functionals can actually be described by using methods that derive from this setting.Publication Open Access Application of two different methods for extending lattice-valued restricted equivalence functions used for constructing similarity measures on L-fuzzy sets(Elsevier, 2018) Palmeira, Eduardo S.; Callejas Bedregal, Benjamin; Bustince Sola, Humberto; Paternain Dallo, Daniel; Miguel Turullols, Laura de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaBased on previous investigations, we have proposed two different methods to extend lattice-valued fuzzy connectives (t-norms, t-conorms, negations and implications) and other related operators, considering a generalized notion of sublattices. Taking into account the results obtained and seeking to analyze the behavior of both extension methods in face of fuzzy operators related to image processing, we have applied these methods so as to extend restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functions. We also generalize the concepts of similarity measure, distance measure and entropy measure for L-fuzzy sets constructing them via restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functionsPublication 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 MatemáticasOrdered 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.Publication 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, PJUPNA1Ordered 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.Publication 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; MatematikaOrdered 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.