Abstract:  Sequential three－way decisions take the advantage of information granularity and various types of costs.Information granularity is the basis of human cognition and decision－making，while costs are usually considered as an important information processing related factor.In this paper，we propose a cost－sensitive sequential three－way decision(S3WD)model，the aim of which is to motivate，interpret and implement the three－way decision(3WD) through the notion of information granularity.We are essentially dealing with three difficulties while applying three－way decisions to cost－sensitive learning.The major difficulty is to construct a sequence of multi－level granularities for 3WD.Multi－granulation represents the information granularity with a partial ordering relation，which provides the semantics for the S3WD model.By constructing a family of equivalence classes of particular object with the change of the number of attributes，a series of coarsening－refinement granularities on information system is formalized.Therefore，we can obtain a complete description of a system with multi－granularity.The second difficulty involves the interpretations of evaluation and thresholds in S3WD.We study decision cost related to information granularity with sequential three－way decisions and focus on the formulations of the cost function according to the principle of coarsening－refinement granulating procedure of information acquirement.The decision cost is composed of the cost of decision result and the cost of decision process，which are two main costs in the cost－sensitive sequential three－way decision model.By utilizing the cost matrix，we construct a reasonable cost structure as evaluation metric for S3WD.The pair of thresholds(α，β)is also obtained.Theoretical analysis indicates that the cost structure has practical and meaningful interpretations of granularity－driven S3WD.The last，crucial difficulty is introducing the objective function to the cost structure.Since there is a trade－off between two costs，we define two optimization problems with the objective of either minimizing the cost of decision result or minimizing the cost of decision process.By solving the optimization problems，the minimal－result－cost S3WD and the minimal－process－cost S3WD are defined as finding optimized S3WD with a minimum cost of decision result or minimum cost of decision process respectively.Two heuristic approaches are designed correspondingly.For minimal－process－cost S3WD，the upper bound of cost of decision result is applied as an input parameter since the optimization problem is a combinational problem.Similar to the minimal－process－cost S3WD，we consider the upper bound of the cost of decision process as a user－defined input parameter for minimal－result－cost S3WD.The two optimization problems represent two risk attitudes of a decision maker in real world scenarios.The experimental results indicate that: 1)with the coarsening－refinement granulating，the cost of the decision result has non－monotonicity subsiding trend，and the cost of the decision process has surging monotonicity trend; 2)with the same number of attributes，the minimal－process－cost S3WD has a higher cost of the decision compared to the minimal－result－cost S3WD; 3)the upper bounds of the costs of the decision result and the upper bounds of the costs of the decision process have directly influence on the decision results; 4)the cost－sensitive S3WD is particularly appropriate for decision－making problems when information is unavailable and costly for on－demand details.