On F-transforms, L-fuzzy partitions and L-fuzzy pretopological spaces

In this paper, we discuss the relationship between the direct lattice-based F-transform and L-fuzzy pretopology. The importance of fuzzy pretopological spaces follows from the fact that they are dense extensions of fuzzy topological spaces, and the corresponding category contains both Top and the category P-Neigh of probabilistic neighbourhood spaces. We show that every direct F↓-transform uniquely determines an L-fuzzy pretopology and discuss the opposite correspondence. In between, some categorical results have been established. Further, some new F-transform theoretic results are studied.

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