Connectedness in L-fuzzy topological spaces

Based on the consideration to the layer structures of fuzzy lattices and the level topologies of L-fuzzy topological spaces, a connectedness is defined for an arbitrary L-fuzzy set in this paper. This definition reflects the degree of connectivity of an L-fuzzy set. It is shown that the connectedness of L-fuzzy topological spaces is an L-good extension, multiplicative and preserved under continuous L-valued Zadeh functions, and that the inverse limit of continuums is a continuum. General L-fuzzy intervals and H(λ)-intervals are defined and connectedness of them are proved. It is also shown that the connectedness of an L-fuzzy topological space is equivalent to the connectedness of its induced I(L)-fuzzy topological space.

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