On level-structure in linear fuzzy neighbourhood spaces (Q2748346)

The authors discuss the level structures of linear fuzzy neighbourhood spaces [\textit{A. K. Katsaras}, Fuzzy Sets Syst. 16, 25-40 (1985; Zbl 0587.54011)]. They show that (1): A linear fuzzy neighbourhood space \((X,{\mathcal N})\) is locally \(n\)-convex if and only if its \(\alpha\)-level space \((X,\iota (t({\mathcal N})))\) is locally convex for all \(\alpha\in [0,1)\); and (2) A linear fuzzy neighbourhood space \((X,{\mathcal N})\) is a (QL)-type fuzzy topological linear space [\textit{C. Wu} and \textit{J. Fang}, Chin. Ann. Math., Ser B 6, 355-364 (1985; Zbl 0578.46011)] if and only if \((X,\iota (t({\mathcal N})))\) is topologically generated.