The rule set which is acquired based on rough set theory can be classified into two categories: deterministic rules and probabilistic rules. Traditional attribute reduction definitions in variable precision rough set model cannot guarantee the rule properties, namely deterministic or probabilistic. In this paper, a new criterion for attribute reduction is put forward based on variable precision rough set model. The rule properties can be preserved during the process of attribute reduction. The relationships between the new reduct definition and available definitions, including Ziarko’s reduct definition and β lower distribution reduct definition are also discussed.