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International Journal of Mathematics and Mathematical Sciences
Volume 28, 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 Hindawi Publishing Corporation. 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 (S(μ),σ(,)) 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.