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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
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