Fuzzy congruences and fuzzy normal subgroups

Abstract A complete description of the congruences on a group in terms of its normal subgroups can be seen in papers by A. Rosenfeld and W. J. Howie. In this paper, we shall introduce the concept of fuzzy congruences on a groupoid and a group, and characterize fuzzy congruences on a group in terms of fuzzy normal subgroups.