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\(L_1\)-space for Sugeno integral. (English) Zbl 1498.28026

Torra, Vicenç (ed.) et al., Modeling decisions for artificial intelligence. 14th international conference, MDAI 2017, Kitakyushu, Japan, October 18–20, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10571, 63-73 (2017).
Summary: Let \(L_1(\mathit{Su})\) be the \(L_1\) space with respect to the Sugeno integral for a fuzzy measure. \(L_1(\mathit{Su})\) is a linear space with the natural quasi-metric. In general \(L_1(\mathit{Su})\) is not necessarily a topological linear space. We shall characterize explicitely the maximal topological linear subspace of \(L_1(\mathit{Su})\).
For the entire collection see [Zbl 1371.68016].

MSC:

28E10 Fuzzy measure theory
46S40 Fuzzy functional analysis
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