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Da Cruz Asmus, Tiago

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Da Cruz Asmus

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Tiago

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Estadƭstica, InformƔtica y MatemƔticas

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0000-0002-7066-7156

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811596

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Now showing 1 - 2 of 2
  • PublicationOpen Access
    A framework for general fusion processes under uncertainty modeling control, with an application in interval-valued fuzzy rule-based classification systems
    (2022) Da Cruz Asmus, Tiago; Sanz Delgado, JosƩ Antonio; Pereira Dimuro, GraƧaliz; Estadƭstica, InformƔtica y MatemƔticas; Estatistika, Informatika eta Matematika
    La fusiĆ³n de informaciĆ³n es el proceso de combinar varios valores numĆ©ricos en uno solo que los represente. En problemas con algĆŗn tipo de modelado difuso, este proceso generalmente se realiza mediante funciones de fusiĆ³n o, su subclase mĆ”s importante, las funciones de agregaciĆ³n. Estas funciones se han aplicado ampliamente en varias tĆ©cnicas para resolver problemas de clasificaciĆ³n, en particular, en los Sistemas de ClasificaciĆ³n Basados en Reglas Difusas (SCBRDs). En este tipo de clasificador, se han aplicado de forma exitosa las funciones de solapamiento (que son funciones de agregaciĆ³n bivariadas con propiedades deseables) y sus generalizaciones n-dimensionales. Cuando hay incertidumbre con respecto al modelado de las funciones de pertenencia en los SCBRDs, generalmente asociados con tĆ©rminos lingĆ¼Ć­sticos, se pueden aplicar conjuntos difusos intervalo-valorados. El modelado de etiquetas lingĆ¼Ć­sticas a travĆ©s de conjuntos difusos intervalo-valorados en los SCBRDs origino a los Sistemas de ClasificaciĆ³n Basados en Reglas Difusas Intervalo-valorados (IV-SCBRDs). En estos sistemas, los procesos de fusiĆ³n se calculan mediante funciones de agregaciĆ³n definidas en el contexto intervalar, mientras que las amplitudes de los intervalos de pertenencia asignados estĆ”n intrĆ­nsecamente relacionadas con la incertidumbre con respecto a los valores que estĆ”n aproximando y, luego, con la calidad de la informaciĆ³n que representan. Sin embargo, no existe una guĆ­a en la literatura que muestre cĆ³mo definir y construir funciones de fusiĆ³n con valores intervalares que tomen en consideraciĆ³n el control de la calidad de la informaciĆ³n. Por todo ello, en esta tesis, desarrollamos un marco para definir funciones de fusiĆ³n intervalo-valoradas n-dimensionales generalizadas considerando los Ć³rdenes admisibles y el control de la calidad de la informaciĆ³n. Aplicamos los conceptos desarrollados en un IV-SCBRD considerado como estado del arte (es decir, IVTURS), desarrollando nuestra propia versiĆ³n basada en operadores de solapamiento con control de la calidad de la informaciĆ³n, demostrando que nuestro enfoque mejora el rendimiento del clasificador. Finalmente, desarrollamos un marco para definir funciones de fusiĆ³n n-dimensionales que actĆŗan en un intervalo real cerrado arbitrario como homĆ³logas de clases conocidas de funciones de fusiĆ³n que actĆŗan sobre el intervalo unitario, para expandir la aplicabilidad de las funciones de fusiĆ³n con propiedades deseables a problemas que no involucren un modelado difuso.
  • PublicationOpen Access
    Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions
    (Elsevier, 2021) Da Cruz Asmus, Tiago; Pereira Dimuro, GraƧaliz; Callejas Bedregal, Benjamin; Sanz Delgado, JosĆ© Antonio; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; EstadĆ­stica, InformĆ”tica y MatemĆ”ticas; Universidad PĆŗblica de Navarra / Nafarroako Unibertsitate Publikoa
    Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. They have been successfully applied as a fuzzy conjunction operation in several problems in which associativity is not required, such as image processing and classification. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees, as in interval-valued fuzzy rule-based classification systems. In this context, the choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of (a,b)-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval and a new notion of increasingness with respect to a pair of partial orders (ā‰¤1,ā‰¤2); (iv) present and compare three construction methods for these width-limited interval-valued overlap functions, considering a pair of orders (ā‰¤1,ā‰¤2), which may be admissible or not, showcasing the adaptability of our developments.