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 Strengthened ordered directional and other generalizations of monotonicity for aggregation functions(Springer, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Lafuente López, Julio; Barrenechea Tartas, Edurne; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaA tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.Publication Open Access Local properties of strengthened ordered directional and other forms of monotonicity(Springer, 2019) Sesma Sara, Mikel; Miguel Turullols, Laura de; Mesiar, Radko; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.Publication Open Access Type-2 fuzzy entropy-sets(IEEE, 2017) Miguel Turullols, Laura de; Santos, Helida; Sesma Sara, Mikel; Callejas Bedregal, Benjamin; Jurío Munárriz, Aránzazu; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaThe final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm.Publication Open Access New measures for comparing matrices and their application to image processing(Elsevier, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Pagola Barrio, Miguel; Burusco Juandeaburre, Ana; Mesiar, Radko; Bustince Sola, Humberto; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work we present the class of matrix resemblance functions, i.e., functions that measure the difference between two matrices. We present two construction methods and study the properties that matrix resemblance functions satisfy, which suggest that this class of functions is an appropriate tool for comparing images. Hence, we present a comparison method for grayscale images whose result is a new image, which enables to locate the areas where both images are equally similar or dissimilar. Additionally, we propose some applications in which this comparison method can be used, such as defect detection in industrial manufacturing processes and video motion detection and object tracking.Publication Open Access Description and properties of curve-based monotone functions(Springer, 2019) Sesma Sara, Mikel; Miguel Turullols, Laura de; Roldán López de Hierro, Antonio Francisco; Špirková, Jana; Mesiar, Radko; Bustince Sola, Humberto; Institute of Smart Cities - ISCCurve-based monotonicity is one of the lately introduced relaxations of monotonicity. As directional monotonicity regards monotonicity along fixed rays, which are given by real vectors, curve-based monotonicity studies the increase of functions with respect to a general curve. In this work we study some theoretical properties of this type of monotonicity and we relate this concept with previous relaxations of monotonicity.Publication Open Access An algorithm for group decision making using n -dimensional fuzzy sets, admissible orders and OWA operators(Elsevier, 2017) Miguel Turullols, Laura de; Sesma Sara, Mikel; Elkano Ilintxeta, Mikel; Asiain Ollo, María José; Bustince Sola, Humberto; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an in- creasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these condi- tions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.