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9.1 It was shown in Chapter II (see Theorem 8.6) that monotone fundamental triangular norm based measures can be decomposed into a sum consisting of a generated measure and a monotonically irreducible measure. Moreover, if the tribe on which the fundamental triangular norm based measure is defined is a generated one, then the monotonically irreducible component is necessarily zero (cf. Theorem 7.1).
KeywordsAdditive Function Fuzzy Subset Absolute Continuity Supporting Hyperplane Jordan Decomposition
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