International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 437-445
Extension on the fuzzy integral based on -decomposable measure
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 13 April 2001
Copyright © 2001 Mamadou Traore. 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 extend the concept of fuzzy integral based on -decomposable measure from nonnegative fuzzy measurable
function to extended real-valued fuzzy measurable function.
Further investigations of fuzzy integrals based on pseudo-additive
decomposable measure are carried out. Meanwhile, the space of all fuzzy measurable function
will be proved to be a pseudo-metric space. Finally, as an
application of this extension the Pettis integral will be
obtained for that kind of fuzzy integral.