Extension of \(n\)-dimensional Euclidean vector space \(E^n\) over \(\mathbb{R}\) to pseudo-fuzzy vector space over \(F_{p}^{1}(1)\) (Q1415088)

The paper deals with fuzzy vector spaces [cf. \textit{A. K. Katsaras} and \textit{D. B. Liu}, J. Math. Anal. Appl. 58, 135--146 (1977; Zbl 0358.46011)] from a geometrical point of view. The author introduces a geometrical interpretation of fuzzy subsets in Euclidean space using the notion of fuzzy points [cf. \textit{S. Gottwald}, Fuzzy Sets Syst. 5, 199--201 (1981; Zbl 0453.54004)]. We have here fuzzy vector arithmetic, fuzzy vector length and distance, fuzzy vector inner product and angle between fuzzy vectors as a generalization of respective notions from Euclidean geometry. However, the author neglects the Hausdorff distance commonly used in fuzzy metric spaces [cf. e.g. \textit{C. X. Wu} and \textit{M. Ma}, Fuzzy Sets Syst. 44, 33--38 (1991; Zbl 0757.46066); ibid. 45, 189--202 (1992; Zbl 0771.46045); ibid. 46, 281--286 (1992; Zbl 0774.54003)].