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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 AB is 0.
MSC:
28A10Real- or complex-valued set functions
28E10Fuzzy measure theory