5 results on '"d-Choquet integral"'
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2. d-XC Integrals: On the Generalization of the Expanded Form of the Choquet Integral by Restricted Dissimilarity Functions and Their Applications.
- Author
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Wieczynski, Jonata, Fumanal-Idocin, Javier, Lucca, Giancarlo, Borges, Eduardo Nunes, Asmus, Tiago da Cruz, Emmendorfer, Leonardo Ramos, Bustince, Humberto, and Dimuro, Gracaliz Pereira
- Subjects
RDF (Document markup language) ,BRAIN-computer interfaces ,INTEGRALS ,GENERALIZATION ,MULTIPLE criteria decision making ,AGGREGATION operators ,STATISTICAL decision making - Abstract
Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustince et al. introduced a generalization of the Choquet integral (CI), called d-Choquet integral, where the authors replaced standard differences with RDFs, providing interesting theoretical results. Motivated by such worthy properties, joint with the excellent performance in applications of other generalizations of the CI (using its expanded form, mainly), this article introduces a generalization of the expanded form of the standard Choquet integral (X-CI) based on RDFs, which we named d-XC integrals. We present not only relevant theoretical results but also two examples of applications. We apply d-XC integrals in two problems in decision making, namely a supplier selection problem (which is a multicriteria decision-making problem) and a classification problem in signal processing, based on motor-imagery brain-computer interface (MI-BCI). We found that two d-XC integrals provided better results when compared to the original CI in the supplier selection problem. Besides that, one of the d-XC integrals performed better than any previous MI-BCI results obtained with this framework in the considered signal processing problem. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. Discrete IV dG-Choquet integrals with respect to admissible orders.
- Author
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Takáč, Zdenko, Uriz, Mikel, Galar, Mikel, Paternain, Daniel, and Bustince, Humberto
- Subjects
- *
CLASSIFICATION - Abstract
In this work, we introduce the notion of d G -Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [ 0 , 1 ] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of d G -Choquet integral are both the discrete Choquet integral and the d -Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with d G -Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. Discrete IV d-Choquet integrals with respect to admissible orders
- Author
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Humberto Bustince, Daniel Paternain, Mikel Galar, Zdenko Takáč, Mikel Uriz, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. ISC - Institute of Smart Cities, Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra. Departamento de Ingeniería Eléctrica, Electrónica y de Comunicación, Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematikak Saila, Nafarroako Unibertsitate Publikoa. Ingeniaritza Elektriko, Elektroniko eta Telekomunikazio Saila, and Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
- Subjects
Work (thermodynamics) ,Pure mathematics ,Logic ,Interval-valued dissimilarity function ,Function (mathematics) ,Fuzzy logic ,Interval-valued fuzzy measure ,Monotone polygon ,Choquet integral ,Artificial Intelligence ,d-Choquet integral ,Mathematics ,Unit interval - Abstract
In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021 This work was supported in part by the Spanish Ministry of Science and Technology, under project PID2019-108392GB-I00 (AEI/10.13039/501100011033), by the project PJUPNA-1926 of the Public University of Navarre and by the project VEGA 1/0267/21 .
- Published
- 2022
5. d-XC integrals: on the generalization of the expanded form of the Choquet integral by restricted dissimilarity functions and their applications
- Author
-
Jonata Wieczynski, Javier Fumanal-Idocin, Giancarlo Lucca, Eduardo Nunes Borges, Tiago da Cruz Asmus, Leonardo Ramos Emmendorfer, Humberto Bustince, Gracaliz Pereira Dimuro, Universidad Pública de Navarra. Departamento de Automática y Computación, Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Nafarroako Unibertsitate Publikoa. Automatika eta Konputazioa Saila, and Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematikak Saila
- Subjects
Multi-criteria decision making ,Computational Theory and Mathematics ,D-Choquet integral ,Artificial Intelligence ,Control and Systems Engineering ,Applied Mathematics ,Motor-imagery brain-computer interface ,Choquet integral ,D-XC integral ,Restricted dissimilarity functions - Abstract
Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustince et al. introduced a generalization of the Choquet integral (CI), called d-Choquet integral, where the authors replaced standard differences with RDFs, providing interesting theoretical results. Motivated by such worthy properties, joint with the excellent performance in applications of other generalizations of the CI (using its expanded form, mainly), this paper introduces a generalization of the expanded form of the standard Choquet integral (X-CI) based on RDFs, which we named d-XC integrals. We present not only relevant theoretical results but also two examples of applications. We apply d-XC integrals in two problems in decision making, namely a supplier selection problem (which is a multi-criteria decision making problem) and a classification problem in signal processing, based on motor-imagery brain-computer interface (MI-BCI). We found that two d-XC integrals provided better results when compared to the original CI in the supplier selection problem. Besides that, one of the d-XC integrals performed better than any previous MI-BCI results obtained with this framework in the considered signal processing problem. This work was supported by Navarra de Servicios y Tecnologías, S.A. (NASERTIC), FAPERGS-Brazil (19/2551-0001279-9, 19/2551-0001660), CNPq-Brazil (301618/2019-4, 305805/2021-5), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB-I00 (MCIN/AEI/10.13039/501100011033)).
- Published
- 2022
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