Honda, Aoi; Okazaki, Yoshiaki \(L_1\)-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 Keywords:\(L_p\)-space; dual space; quasi-metric; fuzzy measure; submeasure; Sugeno integral; translation-invariant metric; quasi-additive functional PDFBibTeX XMLCite \textit{A. Honda} and \textit{Y. Okazaki}, Lect. Notes Comput. Sci. 10571, 63--73 (2017; Zbl 1498.28026) Full Text: DOI