Let i≥2Δ≥01≤a≤b−Δn>(a+b)(ib+2m−2)a+n′ and δ(G)≥b2a+n′+2m, and let g,f be two integer-valued functions defined on V(G) such that a≤g(x)≤f(x)−Δ≤b−Δ for each x∈V(G). In this article, it is determined that G is a fractional (g,f,n′,m)-critical deleted graph if max{d1,d2,···,di}≥b(n+n′)a+b for any independent subset {x1,x2,...,xi}⊆V(G). The result is tight on independent set degree condition.