An attribute reduct, that is, a minimal set of attributes with the same classi cation ability as that of the entire set of attributes, is an important concept in rough set analysis. There are di erent costs associated with attributes, such as money, time and other resources. Costs of an attribute reduct can be classi ed into two categories, namely, process cost and result cost for classi cations. An important task of rough set analysis is to obtain an attribute reduct with a minimal total cost. There are two types of costs. Many studies focus on only one type of costs, that is, process cost or result cost. In this thesis, a general de nition of total-cost-sensitive at- tribute reducts based on the decision-theoretic rough set (DTRS) model is proposed, which uni es recent studies on di erent cost-sensitive attribute reducts. In special cases, the general de nition of total-cost-sensitive attribute reducts can cover process- cost-sensitive attribute reducts and result-cost-sensitive attribute reducts. The con- nection between DTRS and Pawlak rough sets with respect to the general de nition is explicitly investigated. The objective of total-cost-sensitive attribute reducts is to nd an attribute reduct with a minimal total cost, which is interpreted as an optimization problem. An attribute reduct construction algorithm with sequential testing is proposed based on sequential three-way decisions. A heuristic function based on sequential testing is developed to nd an ordering attribute reduct with an approximate minimal total cost and experimental results are demonstrated to support our methods.