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- Title
C∞ L-fuzzy manifolds with L-gradation of openness and C∞ LG-fuzzy mappings of them.
- Authors
Mostafavi, M.
- Abstract
In this paper, we generalize all of the fuzzy structures which we have discussed in [14] to L-fuzzy set theory, where L =< L;≤;∧,∨,' > denotes a complete distributive lattice with at least two elements. We define 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 define C∞ L-fuzzy manifolds with L-gradation of openness and C∞ 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.
- Subjects
MANIFOLDS (Mathematics); DISTRIBUTIVE lattices; SUBMANIFOLDS; SET theory; TOPOLOGICAL spaces; MATHEMATICAL equivalence
- Publication
Iranian Journal of Fuzzy Systems, 2020, Vol 17, Issue 6, p157
- ISSN
1735-0654
- Publication type
Article