1. 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