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Advances in Fuzzy Systems
Volume 2018, Article ID 9730502, 10 pages
Research Article

Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

Department of Mathematics, University of Sultan Moulay Slimane, Laboratory of Applied Mathematics & Scientific Calculus, P.O. Box 523, Beni Mellal, Morocco

Correspondence should be addressed to Elhassan Eljaoui; moc.liamg@ssahiuoajle

Received 14 August 2017; Accepted 27 November 2017; Published 1 January 2018

Academic Editor: Erich Peter Klement

Copyright © 2018 Elhassan Eljaoui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.