Semicomplete Lattice of All T-Complex Gradations of Openness on a Fuzzy Topological Space

‎In this paper‎, ‎we introduce the complex (anti complex) fuzzy topological space (X‎, ‎\mathfrak{T})‎‎with complex (anti complex) gradation of openness under T-norm (C-conorm) which X is itself a T-complex (C-anti complex) fuzzy subset of a nonempty set M‎. ‎We show that the set of all T-complex gradations of openness on X is a semicomplete lattice‎.We give some example such as T-complex fuzzy subspace of \Lambda \mathbb{R}^{m}‎, ‎the exterior algebra on \mathbb{R}^{m}.

Keywords:

Spiral T-norm‎ , ‎T-complex fuzzy subset‎ , ‎C-anti complex fuzzy subspace‎ , ‎complex gradation of openess under T-norm‎ , ‎anti complex fuzzy topological space