Connectedness in L-fuzzy topological spaces

✍ Scribed by Sheng-Gang Li

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 126 KB
• Volume: 116
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00187-0

✦ Synopsis

Based on the consideration to the layer structures of fuzzy lattices and the level topologies of L-fuzzy topological spaces, a connectedness is deÿned for an arbitrary L-fuzzy set in this paper. This deÿnition re ects 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 ( )-intervals are deÿned 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.