S. P. Tiwari - Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad-۸۲۶۰۰۴, Jharkhand, India
I. Perfilieva - University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, NSC IT۴Innovations, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic
A. P. Singh - Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad-۸۲۶۰۰۴, Jharkhand, India

The aim of the present work is to study the  F-transform over a generalized residuated lattice.  We discuss the properties that are common with the F-transform over a residuated lattice. We show that the F^{\uparrow}-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.

Generalized residuated lattice, Fuzzy partition, Direct F-transform, Inverse F-transform