In the past,many large area falling accidents of hard roof occurred in room-and-pillar mining in Datong Coal Mine.According to the characteristics and mechanisms of the roof collapse,considering randomness,heterogeneity and uncertainty of supporting conditions due to the size differences and irregular distribution of pillars as well as the strength difference between pillars,the authors applied fuzzy set theory to study the influences of the nonhomogeneous factors on the lowering process of supporting capacity of pillar-roof system and its failure coefficient.The membership function which represents the nonhomogeneity of supporting conditions between pillars as well as the conditional membership equation for fuzzy failure coefficients of coal-pillar system were presented.At last,the principles how to choose the membership function was discussed.