$F$-type fuzzy topological space; variational principle
The main purpose of this paper is to introduce the concept of $F$-type fuzzy topological spaces. Further variational principle and Caristi’s fixed point theorem have been extended in the $F$-type fuzzy topological spaces.
 Kramosil I., Michálek J.: Fuzzy metric and statistical metric spaces
. Kybernetika 11 (1975), 326–334 MR 0410633