In this paper, we generalize all of the fuzzy structures which we have discussed in \cite{MM} to $L$-fuzzy set theory, where $L= <L,\leq,\bigwedge,\bigvee, '>$ 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.
Mostafavi, M. (2020). $C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them. Iranian Journal of Fuzzy Systems, 17(6), 157-174. doi: 10.22111/ijfs.2020.5608
MLA
M. Mostafavi. "$C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them", Iranian Journal of Fuzzy Systems, 17, 6, 2020, 157-174. doi: 10.22111/ijfs.2020.5608
HARVARD
Mostafavi, M. (2020). '$C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them', Iranian Journal of Fuzzy Systems, 17(6), pp. 157-174. doi: 10.22111/ijfs.2020.5608
VANCOUVER
Mostafavi, M. $C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them. Iranian Journal of Fuzzy Systems, 2020; 17(6): 157-174. doi: 10.22111/ijfs.2020.5608
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