Dpto. Matemáticas - Matematika Saila
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Browsing Dpto. Matemáticas - Matematika Saila by Department/Institute "Institute of Smart Cities - ISC"
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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.Publication Embargo Binary relations coming from solutions of functional equations: orderings and fuzzy subsets(World Scientific Publishing Company, 2017) Campión Arrastia, María Jesús; Miguel Turullols, Laura de; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Abrísqueta Usaola, Francisco Javier; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe 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.Publication Open Access Interval-valued Atanassov intuitionistic OWA aggregations using admissible linear orders and their application to decision making(IEEE, 2016) Miguel Turullols, Laura de; Bustince Sola, Humberto; Pekala, Barbara; Bentkowska, Urszula; Silva, Ivanoska da; Bedregal, Benjamin; Mesiar, Radko; Ochoa Lezaun, Gustavo; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; MatemáticasBased on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study OWA operators in these sets distinguishing between the weights associated to the membership and those associated to the nonmembership degree which may differ from the latter. We also study Choquet integrals for aggregating information which is represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two algorithms to choose the best alternative in a decision making problem when we use this kind of sets to represent information.