Abstract: Rough set theory and fuzzy set theory are complementary generalizations of classical set theory.This paper concerns with rough sets,fuzzy sets and vector spaces.We construct a rough fuzzy ...

Elements of a vector space are called as vectors. A vector space over the field \ (\mathbb {R}\) is called a real vector space, i.e, a vector space which considers scalars as real numbers. Without ...

The objectives of this course are: to develop competence in the basic concepts of linear algebra, including systems of linear equations, vector spaces, subspaces, linear transformations, the ...

The objectives of this course are: to develop competence in the basic concepts of linear algebra, including systems of linear equations, vector spaces, subspaces, linear transformations, the ...

Abstract.Many important examples of topological spaces can be represented as a union of a finite or countable collection of metrizable subspaces. However, it is far from clear which spaces in general ...

Almost everything in one place to start your preparation for your GATE DA. Things are arranged from different sources or created by my. Counting (permutation and combinations), probability axioms, ...

Let ω be a weight on ℤ, and assume that the translation operator S : (un)n∈ℤ → (un–1)n∈ℤ is bounded on ${\mathrm{\ell}}_{\mathrm{\omega }}^{2}\left(\mathrm{\mathbb{Z}}\right)$, and that the spectrum ...