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A fuzzy measure algebra as a metric space. (English) Zbl 0872.28012
Summary: We extend to fuzzy subset setting the results from classical measure theory that (i) a measure algebra \((a,\mu)\) with its canonical metric \(\rho\) is a complete metric space for which the mappings \(A\to A'\), \((A,B)\to A\vee B\), \((A,B)\to A\wedge B\) are uniformly continuous, and (ii) \((a,\rho)\) is a convex metric space iff \(a\) is nonatomic. The classical results are particular cases of the extensions.

MSC:
28E10 Fuzzy measure theory
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