A first approach to an axiomatic model of multi-measures

We establish an axiomatic model of multi-measures, capturing some classes of measures studied in the fuzzy sets literature, where they are applied to only one or two arguments

Optimization of the tantalum ore production by control the milling process

Tantalum is a strategic metal with multiple applications in the new technologies. Tantalum deposits are scarce in EU. Thus, more efficient extracting processes are necessary to contribute to major European independency on these critical raw materials. Tantalum occurs mainly in pegmatites and leucogranite deposits and its placers. Europe does not produce tantalum; however, several deposits are susceptible of being exploited if technologies of processing are improved. This work is part of the Optimore Project which aims to develop modelling and control technologies, using advanced sensing and advanced industrial control by using artificial intelligence techniques, for the more efficient and flexible tantalum and tungsten processing from crushing to separation process. In this paper, a preliminary study of characterization of tantalum ores from leucogranite and alluvial deposits is presented to be used as a base for design the milling experiments to optimize the tantalum recovering during the processing. In the ore deposits tantalum appears in solid solution with niobium in complex oxides, which forms low grade aggregates which need to be processed by means of a separation process. Tantalum ores characterised here belong to alluvial placers of pegmatitic origin located in the Bolivian Amazon Craton and to leocogranites of Penuota, in Spain. Ta bearing minerals of the Bolivian placers are mainly from the columbite group minerals. In Penouta microlite is abundant and often it has a zoning characterised by a Nb-rich core followed by a Ta-rich rim of several cm in thickness.Peer ReviewedPostprint (published version

Role of age and comorbidities in mortality of patients with infective endocarditis

[Purpose]: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. [Methods]: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015.Patients were stratified into three age groups:<65 years,65 to 80 years,and ≥ 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. [Results]: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 ≥ 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients ≥80 years who underwent surgery were significantly lower compared with other age groups (14.3%,65 years; 20.5%,65-79 years; 31.3%,≥80 years). In-hospital mortality was lower in the <65-year group (20.3%,<65 years;30.1%,65-79 years;34.7%,≥80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%,≥80 years; p = 0.003).Independent predictors of mortality were age ≥ 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI ≥ 3 (HR:1.62; 95% CI:1.39–1.88),and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared,the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. [Conclusion]: There were no differences in the clinical presentation of IE between the groups. Age ≥ 80 years, high comorbidity (measured by CCI),and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group

Contribución al estudio de ternas de De Morgan generalizadas

Los orígenes de la Lógica Matemática ó Álgebra de la Lógica se sitúan en el trabajo de G. Boole "The Mathematical Analysis of Logic" (Mac Millan, Barclay £ Mac Millan, Cambridge, 1847). Con la aportación de Boole se llegan a construir los sistemas formales necesarios para deducir los teoremas de la lógica a través de procedimientos puramente algebraicos. Así al dotar a la Lógica de un instrumento algebraico aparecen las Algebras de Boole que modelizan la Lógica Clásica, y todas las variaciones que de ésta han ido surgiendo, han dado lugar a nuevas estructuras algebraicas. De la Lógica Intuicionista nacen las Algebras de Heyting; de la Lógica Polivalente de Luckasiewicz nacen las álgebras de De Morgan, etc., teniendo así la posibilidad de hacer corresponder a cada Lógica una estructura característica. Todas las estructuras citadas que se enmarcan dentro de la Lógica Clásica ó Booleana tienen como estructura básica la de retículo, no ocurre lo mismo con todas y cada una de las estructuras que se derivan de la Lógica Polivalente. La teoría de Conjuntos Difusos (Zadeh, 1965] , que resulta ser en cierto sentido una generalización de la teoría de Conjuntos Clásicos, permite utilizar operadores conjunción y disyunción con los que ya no se mantiene la estructura reticular, consiguiéndose estructuras algebraicas más flexibles; la estructura básica que se mantiene con estos conectivos (junto con el complementario definido por medio de funciones de negación fuerte) es la llamada Terna de De Morgan. Desde el trabajo de Zadeh que dio origen a la teoría de los Conjuntos I difusos, han ido apareciendo los trabajos de [R. Bellman y M. Giertz, 1973], [E. Trillas, 1979, 1980] , [c. Alsina, 198oJ , [F. Esteva, 1981J , [C. Alsina, E. Trillas y L. Valverde, 1982, 1983J , [T. Riera, 1978] , ¡G. Mayor, 1984J , entre otros. Tomando como punto de partida las citadas ternas de De Morgan en esta memoria se presenta un estudio de las ternas, aquí introducidas y llamadas "Ternas de De Morgan Generalizadas". Estas han sido construidas con la combinación de distintos operadores, como son las t-normas, t-conormas, funciones de agregación, medias casi-aritmeticas y las funciones Le, que en algún sentido genralizan los conectivos "y" y "o", junto con una negación fuerte que generaliza el "no". La memoria consta de cinco capítulos. En el capítulo I nos ocupamos, en distintas secciones, de la introducción de los diferentes tipos de ternas de De Morgan Generalizadas, así como de algunas propiedades que resultan de interés y del estudio de los automorfismos entre cada una de las clases de las citadas ternas. Además, en cada una de las secciones aparecen los conceptos básicos necesarios para el desarrollo de las mismas, y del trabajo de toda la memoria. El capítulo II está dedicado al estudio de la propiedad de absorción de la teoría de Conjuntos Clásicos en las ternas de De Morgan Generalizadas; dicho trabajo se divide en dos secciones, la primera resume el estudio de la propiedad citada sobre las Principales ternas de De Morgan Generalizadas, y la segunda sobre las llamadas ternas de De Morgan Mixtas. La última sección del capítulo, que en cierto sentido completa las anteriores recoge los resultados obtenidos al considerar las propiedades (desigualdades) de sub-absorción y super-absorción que se deducen de la propiedad de absorción de las dos secciones anteriores. II En el capítulo III se estudia la propiedad distributiva en las ternas de De Morgan Generalizadas; dicho trabajo se presenta en dos secciones con el mismo criterio del capítulo anterior, aunque el número de resultados excede en mucho a los del segundo capítulo. El capítulo IV presenta un amplio estudio de la conocida relación: (AnB)U(AOB )=A de la teoría de los Conjuntos Clásicos, en las ternas de De Morgan Generalizadas; tomando como punto de partida el trabajo de C. Alsina (1985), y la introducción de un nuevo lema que resulta ser básico en el desarrollo de todo el capítulo. En el capítulo V se lleva a cabo la "interpretación" a la luz de las estructuras estudiadas, de conceptos que hacen referencia a la teoría de Conjuntos Difusos, como son el de Entropía, Métricas, Indistinguibülidad, Casi-implicaciones y Relaciones Borrosas. El trabajo de éste capítulo se divide en cuatro secciones, en la primera de ellas nos ocupamos de definir entropías con algunos de los operadores introducidos en el primer capítulo. En la segunda sección se agrupa el estudio de las métricas con él de los operadores de Indsitinguibilidad, por la relación que existe entre ellos (E. Trillas, 19 82* . En la tercera sección aparece un estudio sobre las Casi-implicaciones, introducidas en dicha sección y termina con una referencia a- la principal regla de inferencia como es el Modus Ponens. En la cuarta y última sección nos ocupamos de la introducción y estudio de las relaciones borrosas, cuya línea de trabajo a seguir se basa en la definición de diferentes tipos especiales, aunque análogos, de producto de matrices, y su posterior desarrollo en función de las propiedades de las distintas relaciones a estudio. La mayor parte de los resultados obtenidos lo han sido gracias a la resolución de un gran número de ecuaciones funcionales, técnica III ésta que destaca en toda la memoria. Termina la memoria con una bibliografía que recoge los articulos y libros utilizados en el desarrollo de nuestro trabajo

Fractal negations

From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R², we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations

On the representation of local indistinguishability operators

This paper studies local indistinguishability operators, i.e., symmetric and transitive fuzzy relations that do not need to be reflexive. This is an important generalization of global indistinguishability relations (fuzzy relations satisfying the reflexivity property in addition) because there are interesting families of fuzzy relations that are non-reflexive. One case are decomposable relations, that are generated by a fuzzy subset and contains the t-norms as an important subfamily. Also the relations associated naturally to fuzzy subgroups are local indistinguishability operators. In this paper these relations will be studied stressing the way they can be generated. A representation theorem will be proved and related to the concepts of extensionality and of fuzzy rough set. Decomposable local indistinguishability operators will also be studied and related with one-dimensional ones in the sense of the previous representation theorem. The presence of these relations in the study of fuzzy subgroups will also be analyzed.Peer ReviewedPostprint (author's final draft

Fractal negations

From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R², we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations

Fractal negations

From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R², we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations

Aggregation of partial T-indistinguishability operators and partial pseudo-metrics

[eng] In this contribution we address our attention on the aggregation of partial T-indistinguishability operators (relations) and partial pseudo-metrics. A characterization of those functions that allow to merge a collection of partial T-indistinguishability operators into a new one was provided by Calvo et al. in [10]by means of (T, TM)-tuples, but here we present another characterization in terms of (+, max)-tuples. Also, we analyze the aggregation of a collection (Ei) ni=1of partial Ti-indistinguishability operators. Moreover, we provide that a generalized inter-exchange composition functions condition is a sufficient condition to guarantee that a function merges partial Ti-indistinguishability operators into a single one. In addition, we give different expressions of those aggregation functions that are object of our study, most of them are defined by means of the additive generators of the corresponding t-norms and another particular function. We see that the functions, that merge partial S-pseudo-metrics into a new one, are related to the functions that aggregate partial pseudo-metrics. Finally, we show the relation between the functions, that merge partial T-indistinguishability operators and the functions that preserve the partial T^∗-pseudo-metrics in the aggregation process

Weighted sums of aggregation operators

he aim of this work is to investigate when a weighted sum, or in other words, a linear combination, of two or more aggregation operators leads to a new aggregation operator. For weights belonging to the real unit interval, we obtain a convex combination and the answer is known to be always positive. However, we will show that also other weights can be used, depending upon the aggregation operators involved. A first set of suitable weights is obtained by a general method based on the variation of the partial derivatives of the aggregation operators. When considering the combination of OWA operators only, all suitable weights can be determined. These results are described explicitly for the case of two aggregation operators, and also for the case of two and three OWA operators