Adapted Fuzzy Integral: An Application in the Finite Element Method

Daniel Sánchez, Luana T. Bassani, Laécio C. Barros, Estevão Esmi

Abstract


In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule.


Keywords


Fuzzy Measure, Sugeno Integral, Finite Element Method, Boundary Value Problem.

References


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DOI: https://doi.org/10.5540/tema.2018.019.01.147

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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