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(lambda)-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. (C) 2000 Elsevier Science B.V. All rights reserved.
connectedness inverse limit l-fuzzy interval h(lambda)-interval induced i(l)-fuzzy topological space fuzzy topology l-fuzzy continuum