Abstract: This paper discussed the problem of attributes reduction in rough set．We first introduced both induced matrix and λ-cut matrix of equivalence relation matrix to calculate upper and lower approximation of decision tables and then proposed a reduction algorithm of positive domain for decision table based on relationship matrix with the prove of correctness in theory．What’s more,a heuristic reduction of attribute core in rough set was proposed to calculate the minimum reduction．With dynamical updating of attributes,we updated attribute equivalence relationship matrix through the method of update of matrix and calculated the positive domain after update of attribute rapidly．The example confirms the feasibility and effectiveness of proposed operation and method of attribute reduction.

Key words: Rough set,Decision tables,Positive domain reduction,Relation matrix