Two properties of fuzzy subquasigroups of a quasigroup

In a recent paper, Biswas (1996) studies two properties of fuzzy subrings of a ring. We extend them to quasigroups and to a certain generalization thereof. In its most basic form the first property is that a fuzzy subquasigroup R of a quasigroup satisfies R(a·a′)=min(R(a),R(a′)) whenever R(a)≠R(a′). The second property relates the cardinalities of level sets of R.