... let X andYbe subsets ofR.In a relationr, an instance ofR,for X- valuezwe defineXr (x) = {x& apos;l::3tEr, such thatt [X] = x& apos;, x ~ x& apos;}.Yr (x) ={YI::3tEr, such thatt [X] EXr (X) , ... meansVxEdl):lx'Edz) : x, , x& apos;,and vice versaVj :DjEXZ.(2) meansVxEdlj:lx'EdZj: x, , x& apos;,and vice versaVJ' :D)EY.So we haveVxEdlj:lx'Edz):z>« x& apos;,and ... writetdX] ~ tz [X] ifVxEdlj:lx'EdZj: x, , x& apos;,and vice versa, i.e.VxEdZj:lx'Edlj: x, , x& apos;,Vj :AjE X. Definition4.1. A fuzzy functional dependency X ~ Y is said...