Raventós Pujol, Armajac
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Raventós Pujol
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Armajac
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Estadística, Informática y Matemáticas
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Publication 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; CienciasDifferent 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.Publication Open Access Unexpected thresholds from independence of irrelevant alternatives in fuzzy arrow theorems(2019) Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y MatemáticasIt is well known Arrow Theorem and its impact into Social Choice. It states that under an apparently mild set of conditions no rule fusing individual preferences into a social one is possible. In order to solve this situation, a possibility is to skip from dichotomic preferences to fuzzy ones. All conditions imposed to aggregation rules should be adapted to the fuzzy setting and due to the existence of different generalizations for each condition, depending on the chosen combination, a possibility or an impossibility result arises. In addition, in case we find a reasonable fuzzy aggregation rule, in most situations dichotomic decisions have to be taken at the end of the day, so the use of thresholds over fuzzy preferences is compulsory to make any decision. Surprisingly, independence of irrelevant alternatives axioms induce different thresholds which, besides they can be used on discrete and dichotomic decision making, transform fuzzy spaces of preferences and its aggregation functions into discrete ones allowing the application of new techniques to their study.Publication 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 MatemáticasA 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.