Adapted Fuzzy Integral: An Application in the Finite Element Method

Authors

  • Daniel Sánchez Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, R. Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brasil. Campus Patagonia, Universidad Austral de Chile, Coyhaique, Chile.
  • Luana T. Bassani Departamento de Matemática Aplicada, IME, Universidade de São Paulo, R. Matão, 1010, 05508-090, São Paulo, SP, Brasil.
  • Laécio C. Barros Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, R. Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brasil.
  • Estevão Esmi Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas, R. Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brasil.

DOI:

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

Keywords:

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

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.

References

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Published

2018-05-05

How to Cite

Sánchez, D., Bassani, L. T., Barros, L. C., & Esmi, E. (2018). Adapted Fuzzy Integral: An Application in the Finite Element Method. Trends in Computational and Applied Mathematics, 19(1), 147. https://doi.org/10.5540/tema.2018.019.01.147

Issue

Vol. 19 No. 1 (2018)

Section

Original Article

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