FUZZY VECTOR-SPACES

This paper defines a basis for a fuzzy vector space and its dimension. A class of fuzzy vector spaces having dimension is introduced, and two standard results from crisp theory are proved for this case, namely di-approximately-m(mu-E1 + mu-E2) = di-approximately-m(mu-E1) + di-approximately-m(mu-E2) - di-approximately-m(mu-E1 AND mu-E2) and di-approximately-m(im-approximately-f) = di-approximately-m(mu-E) - di-approximately-m(ke-approximately-r f-approximately). The product of two fuzzy vector spaces under certain conditions is also characterized.