C1 L-fuzzy manifolds with L-gradation of openness and C1 LG-fuzzy mappings of them

In this paper, we generalize all of the fuzzy structures which we have discussed in [14] to L-fuzzy set theory, where L =< L;; V ; W ;0 > denotes a complete distributive lattice with at least two elements. We dene the concept of an LG-fuzzy topological space (X;T) which X is itself an L-fuzzy subset of a crisp set M and T is an L-gradation of openness of L-fuzzy subsets of M which are less than or equal to X. Then we dene C1 L-fuzzy manifolds with L-gradation of openness and C1 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 dene 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.