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Zbl 1155.28300
Tanaka, Jun
Hahn decomposition theorem of signed fuzzy measure. (English)
[J] Adv. Fuzzy Sets Syst. 3, No. 3, 315-323 (2008). ISSN 0973-421X

Summary: We define a signed fuzzy measure on s-algebras as well as define positive and negative fuzzy sets. Herein, we will show that the Fuzzy Hahn Decomposition Theorem decomposes any space $X$ into a positive fuzzy set $A$ and a negative fuzzy set $B$ such that $A+B=X$ and the signed fuzzy measure of $A\land B$ is 0.
MSC 2000:
*28A10 Real- or complex-valued set functions
28E10 Fuzzy measures

Keywords: fuzzy measure; signed measure; Hahn decomposition; fuzzy sets

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