In classic decision-theoretic rough sets (DTRS), the cost objective function of three-way decision is typical monotone linear function. However, it is usually found that the functional relationship between delay decision's cost and probability is non monotonic in practical experience. Hence, the classical cost sensitive three-way decision model in DTRS is not suitable for modeling and reasoning this non monotonic phenomenon. In order to solve the non-monotonic phenomena in the cost sensitive three-way decision problem, a novel piece-wise delay cost sensitive three-way decision model is proposed based on the classical positive/negative domain decision loss functions. The novel model defines two different sets of delay decision loss functions which have the characteristics of monotonous increase and monotonic decrease, and constructs segmented delay three-way decision cost objective function systems, measurement indexes, and segment decision strategies. Then, on the basis of the relationship among conditional probability, loss function and basic metrics, segmented delay cost sensitivity three-way decision model is proposed, and the corresponding three-way classification thresholds reasoning are implemented. Finally, a group of typical analysis examples are used to verify the feasibility of the segmented delay cost sensitivity three-way decision model and its classification.