Fuzzy topological vector spaces over \(\overline{R}\) (Q1304278)

The authors give the definition of fuzzy vector in a topological vector space as extension of the notion of fuzzy number over the reals, diversifying from the approach of \textit{A. K. Katsaras} [ibid. 6, 85-95 (1981; Zbl 0463.46009)]. The authors define the concept of fuzzy vector space over the reals and give suitable examples. The main aim of the paper is the concept of fuzzy topological vector space, on which a suitable topology is given in such a way that it is compatible with the underlying algebraic structure, so extending an analogous concept of \textit{P. Diamond} and \textit{P. E. Kloeden} [``Metric spaces of fuzzy sets: theory and applications'', World Scientific (1994; Zbl 0873.54019)].