Babu, Sundar S; Dr.Thrivikraman, T(Cochin University Of Science And Technology, March 21, 1989)
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Abstract:
It is believed that every fuzzy generalization should be
formulated in such a way that it contain the ordinary set
theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9]
with an arbitrary complete and distributive lattice as the
membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy
topologies on a set. It is proved that in general, the
lattice of fuzzy topologies is not complemented. Complements
of some fuzzy topologies are found out. It is observed that
(L,X) is not uniquely complemented. However, a complete
analysis of the problem of complementation in the lattice
of fuzzy topologies is yet to be found out
Description:
Depantment of Mathematics and Statistics
Cochin University of Scince
and Technology