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Hahn decomposition theorem of signed fuzzy measure. (English) Zbl 1155.28300
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:
 28A10 Real- or complex-valued set functions 28E10 Fuzzy measure theory
##### Keywords:
fuzzy measure; signed measure; Hahn decomposition; fuzzy sets
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