Connectedness in L-fuzzy topological spaces

Based on the consideration to the layer structures of fuzzy lattices and th e level topologies of L-fuzzy topological spaces, a connectedness is define d 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 connectednes s of L-fuzzy topological spaces is an L-good extension, multiplicative and preserved under continuous L-valued Zadeh functions, and that the inverse l imit of continuums is a continuum. General L-fuzzy intervals and H(lambda)- intervals are defined and connectedness of them are proved. It is also show n that the connectedness of an L-fuzzy topological space is equivalent to t he connectedness of its induced I(L)-fuzzy topological space. (C) 2000 Else vier Science B.V. All rights reserved.