On flags and fuzzy subspaces of vector spaces

This paper deals with fuzzy subspaces of a vector space in terms of flags. We define the operations sum, product, tensor product, Hom, and intersection of fuzzy subspaces and in each case we characterise the corresponding flag. Some of these have been considered in the literature in different context. The novelty of this paper is in the use of flags as primary tool to study fuzzy subspaces.