C^\infty L-fuzzy manifolds with L-gradation of openness and C^\infty LG-fuzzy mappings of them

In this paper, we generalize all of the fuzzy structures which we have discussed in \cite{MM} to L-fuzzy set theory, where L= denotes a complete distributive lattice with at least two elements. We define the concept of an LG-fuzzy topological space (X, \mathfrak{T} ) which X is itself an L-fuzzy subset of a crisp set M and \mathfrak{T} is an L-gradation of openness of L-fuzzy subsets of M which are less than or equal to X . Then we define C^\infty L-fuzzy manifolds with L-gradation of openness and C^\infty LG-fuzzy mappings of them such as LG-fuzzy immersions and LG-fuzzy imbeddings. We fuzzify the concept of the product manifolds with L-gradation of openness and define LG-fuzzy quotient manifolds when we have an equivalence relation on M and investigate the conditions of the existence of the quotient manifolds. We also introduce LG-fuzzy immersed, imbedded and regular submanifolds.

Keywords:

C^infty LG-fuzzy n-manifolds , C^infty LG -fuzzy mappings , LG-fuzzy quotient manifolds , LG-fuzzy immersion , regular LG-fuzzy submanifolds