A note on specialization L-preorder of L-topological spaces, L-fuzzifying topological spaces, and L-fuzzy topological spaces

Authors:
Wei Yao;Fu-Gui Shi
Affiliations:
Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050054, Hebei, PR China and Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865-1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies, Internat. J. Approx. Reasoning 48 (2008) 98-109] are special cases of that of L-fuzzy topological spaces introduced by Fang [I-fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems 158 (2007) 2359-2374].